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Optical telescope

An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.

There are three primary types of optical telescope:
 * Refracting telescopes, which use lenses and less commonly also prisms (dioptrics)
 * Reflecting telescopes, which use mirrors (catoptrics)
 * Catadioptric telescopes, which combine lenses and mirrors

An optical telescope's ability to resolve small details is directly related to the diameter (or aperture) of its objective (the primary lens or mirror that collects and focuses the light), and its light-gathering power is related to the area of the objective. The larger the objective, the more light the telescope collects and the finer detail it resolves.

People use optical telescopes (including monoculars and binoculars) for outdoor activities such as observational astronomy, ornithology, pilotage, hunting and reconnaissance, as well as indoor/semi-outdoor activities such as watching performance arts and spectator sports.

History
The telescope is more a discovery of optical craftsmen than an invention of a scientist. The lens and the properties of refracting and reflecting light had been known since antiquity, and theory on how they worked was developed by ancient Greek philosophers, preserved and expanded on in the medieval Islamic world, and had reached a significantly advanced state by the time of the telescope's invention in early modern Europe. But the most significant step cited in the invention of the telescope was the development of lens manufacture for spectacles, first in Venice and Florence in the thirteenth century, and later in the spectacle making centers in both the Netherlands and Germany. It is in the Netherlands in 1608 where the first documents describing a refracting optical telescope surfaced in the form of a patent filed by spectacle maker Hans Lippershey, followed a few weeks later by claims by Jacob Metius, and a third unknown applicant, that they also knew of this "art".

Word of the invention spread fast and Galileo Galilei, on hearing of the device, was making his own improved designs within a year and was the first to publish astronomical results using a telescope. Galileo's telescope used a convex objective lens and a concave eye lens, a design is now called a Galilean telescope. Johannes Kepler proposed an improvement on the design that used a convex eyepiece, often called the Keplerian Telescope.

The next big step in the development of refractors was the advent of the Achromatic lens in the early 18th century, which corrected the chromatic aberration in Keplerian telescopes up to that time—allowing for much shorter instruments with much larger objectives.

For reflecting telescopes, which use a curved mirror in place of the objective lens, theory preceded practice. The theoretical basis for curved mirrors behaving similar to lenses was probably established by Alhazen, whose theories had been widely disseminated in Latin translations of his work. Soon after the invention of the refracting telescope, Galileo, Giovanni Francesco Sagredo, and others, spurred on by their knowledge that curved mirrors had similar properties to lenses, discussed the idea of building a telescope using a mirror as the image forming objective. The potential advantages of using parabolic mirrors (primarily a reduction of spherical aberration with elimination of chromatic aberration) led to several proposed designs for reflecting telescopes, the most notable of which was published in 1663 by James Gregory and came to be called the Gregorian telescope, but no working models were built. Isaac Newton has been generally credited with constructing the first practical reflecting telescopes, the Newtonian telescope, in 1668 although due to their difficulty of construction and the poor performance of the speculum metal mirrors used it took over 100 years for reflectors to become popular. Many of the advances in reflecting telescopes included the perfection of parabolic mirror fabrication in the 18th century, silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century, segmented mirrors to allow larger diameters, and active optics to compensate for gravitational deformation. A mid-20th century innovation was catadioptric telescopes such as the Schmidt camera, which uses both a lens (corrector plate) and mirror as primary optical elements, mainly used for wide field imaging without spherical aberration.

The late 20th century has seen the development of adaptive optics and space telescopes to overcome the problems of astronomical seeing.

The electronics revolution of the early 21st century led to the development of computer-connected telescopes in the 2010s that allow non-professional skywatchers to observe stars and satellites using relatively low-cost equipment by taking advantage of digital astrophotographic techniques developed by professional astronomers over previous decades. An electronic connection to a computer (smartphone, pad, or laptop) is required to make astronomical observations from the telescopes. The digital technology allows multiple images to be stacked while subtracting the noise component of the observation producing images of Messier objects and faint stars as dim as an apparent magnitude of 15 with consumer-grade equipment.

Principles
The basic scheme is that the primary light-gathering element, the objective (1) (the convex lens or concave mirror used to gather the incoming light), focuses that light from the distant object (4) to a focal plane where it forms a real image (5). This image may be recorded or viewed through an eyepiece (2), which acts like a magnifying glass. The eye (3) then sees an inverted, magnified virtual image (6) of the object.

Inverted images
Most telescope designs produce an inverted image at the focal plane; these are referred to as inverting telescopes. In fact, the image is both turned upside down and reversed left to right, so that altogether it is rotated by 180 degrees from the object orientation. In astronomical telescopes the rotated view is normally not corrected, since it does not affect how the telescope is used. However, a mirror diagonal is often used to place the eyepiece in a more convenient viewing location, and in that case the image is erect, but still reversed left to right. In terrestrial telescopes such as spotting scopes, monoculars and binoculars, prisms (e.g., Porro prisms) or a relay lens between objective and eyepiece are used to correct the image orientation. There are telescope designs that do not present an inverted image such as the Galilean refractor and the Gregorian reflector. These are referred to as erecting telescopes.

Design variants
Many types of telescope fold or divert the optical path with secondary or tertiary mirrors. These may be integral part of the optical design (Newtonian telescope, Cassegrain reflector or similar types), or may simply be used to place the eyepiece or detector at a more convenient position. Telescope designs may also use specially designed additional lenses or mirrors to improve image quality over a larger field of view.

Characteristics
Design specifications relate to the characteristics of the telescope and how it performs optically. Several properties of the specifications may change with the equipment or accessories used with the telescope; such as Barlow lenses, star diagonals and eyepieces. These interchangeable accessories do not alter the specifications of the telescope, however they alter the way the telescope's properties function, typically magnification, apparent field of view (FOV) and actual field of view.

Surface resolvability
The smallest resolvable surface area of an object, as seen through an optical telescope, is the limited physical area that can be resolved. It is analogous to angular resolution, but differs in definition: instead of separation ability between point-light sources it refers to the physical area that can be resolved. A familiar way to express the characteristic is the resolvable ability of features such as Moon craters or Sun spots. Expression using the formula is given by twice the resolving power $$R$$ over aperture diameter $$D$$ multiplied by the objects diameter $$D_{ob}$$ multiplied by the constant $$\Phi$$ all divided by the objects apparent diameter $$D_{a}$$.

Resolving power $$R$$ is derived from the wavelength $${\lambda}$$ using the same unit as aperture; where 550 nm to mm is given by: $$R = \frac{\lambda}{10^6} = \frac{550}{10^6} = 0.00055$$.

The constant $$\Phi$$ is derived from radians to the same unit as the object's apparent diameter; where the Moon's apparent diameter of $$D_{a} = \frac{313\Pi}{10800}$$ radians to arcsecs is given by: $$D_{a} = \frac{313\Pi}{10800} \cdot 206265 = 1878$$.

An example using a telescope with an aperture of 130 mm observing the Moon in a 550 nm wavelength, is given by: $$F = \frac{\frac{2R}{D} \cdot D_{ob} \cdot \Phi}{D_{a}} = \frac{\frac{2 \cdot 0.00055}{130} \cdot 3474.2 \cdot 206265}{1878} \approx 3.22$$

The unit used in the object diameter results in the smallest resolvable features at that unit. In the above example they are approximated in kilometers resulting in the smallest resolvable Moon craters being 3.22 km in diameter. The Hubble Space Telescope has a primary mirror aperture of 2400 mm that provides a surface resolvability of Moon craters being 174.9 meters in diameter, or sunspots of 7365.2 km in diameter.

Angular resolution
Ignoring blurring of the image by turbulence in the atmosphere (atmospheric seeing) and optical imperfections of the telescope, the angular resolution of an optical telescope is determined by the diameter of the primary mirror or lens gathering the light (also termed its "aperture").

The Rayleigh criterion for the resolution limit $$\alpha_R$$ (in radians) is given by
 * $$\sin(\alpha_R) = 1.22 \frac{\lambda}{D}$$

where $$\lambda$$ is the wavelength and $$D$$ is the aperture. For visible light ($$\lambda$$ = 550 nm) in the small-angle approximation, this equation can be rewritten:
 * $$\alpha_R = \frac{138}{D}$$

Here, $$\alpha_R$$ denotes the resolution limit in arcseconds and $$D$$ is in millimeters. In the ideal case, the two components of a double star system can be discerned even if separated by slightly less than $$\alpha_R$$. This is taken into account by the Dawes limit
 * $$\alpha_D = \frac{116}{D}$$

The equation shows that, all else being equal, the larger the aperture, the better the angular resolution. The resolution is not given by the maximum magnification (or "power") of a telescope. Telescopes marketed by giving high values of the maximum power often deliver poor images.

For large ground-based telescopes, the resolution is limited by atmospheric seeing. This limit can be overcome by placing the telescopes above the atmosphere, e.g., on the summits of high mountains, on balloons and high-flying airplanes, or in space. Resolution limits can also be overcome by adaptive optics, speckle imaging or lucky imaging for ground-based telescopes.

Recently, it has become practical to perform aperture synthesis with arrays of optical telescopes. Very high resolution images can be obtained with groups of widely spaced smaller telescopes, linked together by carefully controlled optical paths, but these interferometers can only be used for imaging bright objects such as stars or measuring the bright cores of active galaxies.

Focal length and focal ratio
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus. A system with a shorter focal length has greater optical power than one with a long focal length; that is, it bends the rays more strongly, bringing them to a focus in a shorter distance. In astronomy, the f-number is commonly referred to as the focal ratio notated as $$N$$. The focal ratio of a telescope is defined as the focal length $$f$$ of an objective divided by its diameter $$D$$ or by the diameter of an aperture stop in the system. The focal length controls the field of view of the instrument and the scale of the image that is presented at the focal plane to an eyepiece, film plate, or CCD.

An example of a telescope with a focal length of 1200 mm and aperture diameter of 254 mm is given by: $$N = \frac {f}{D} = \frac {1200}{254} \approx 4.7$$

Numerically large Focal ratios are said to be long or slow. Small numbers are short or fast. There are no sharp lines for determining when to use these terms, and an individual may consider their own standards of determination. Among contemporary astronomical telescopes, any telescope with a focal ratio slower (bigger number) than f/12 is generally considered slow, and any telescope with a focal ratio faster (smaller number) than f/6, is considered fast. Faster systems often have more optical aberrations away from the center of the field of view and are generally more demanding of eyepiece designs than slower ones. A fast system is often desired for practical purposes in astrophotography with the purpose of gathering more photons in a given time period than a slower system, allowing time lapsed photography to process the result faster.

Wide-field telescopes (such as astrographs), are used to track satellites and asteroids, for cosmic-ray research, and for astronomical surveys of the sky. It is more difficult to reduce optical aberrations in telescopes with low f-ratio than in telescopes with larger f-ratio.

Light-gathering power
The light-gathering power of an optical telescope, also referred to as light grasp or aperture gain, is the ability of a telescope to collect a lot more light than the human eye. Its light-gathering power is probably its most important feature. The telescope acts as a light bucket, collecting all of the photons that come down on it from a far away object, where a larger bucket catches more photons resulting in more received light in a given time period, effectively brightening the image. This is why the pupils of your eyes enlarge at night so that more light reaches the retinas. The gathering power $$P$$ compared against a human eye is the squared result of the division of the aperture $$D$$ over the observer's pupil diameter $$D_{p}$$, with an average adult having a pupil diameter of 7 mm. Younger persons host larger diameters, typically said to be 9 mm, as the diameter of the pupil decreases with age.

An example gathering power of an aperture with 254 mm compared to an adult pupil diameter being 7 mm is given by: $$P = \left(\frac {D}{D_{p}}\right)^2 = \left(\frac {254}{7}\right)^2 \approx 1316.7$$

Light-gathering power can be compared between telescopes by comparing the areas $$A$$ of the two different apertures.

As an example, the light-gathering power of a 10-meter telescope is 25x that of a 2-meter telescope: $$p = \frac {A_{1}}{A_{2}} = \frac {\pi5^2}{\pi1^2} = 25$$

For a survey of a given area, the field of view is just as important as raw light gathering power. Survey telescopes such as the Large Synoptic Survey Telescope try to maximize the product of mirror area and field of view (or etendue) rather than raw light gathering ability alone.

Magnification
The magnification through a telescope makes an object appear larger while limiting the FOV. Magnification is often misleading as the optical power of the telescope, its characteristic is the most misunderstood term used to describe the observable world. At higher magnifications the image quality significantly reduces, usage of a Barlow lens increases the effective focal length of an optical system—multiplies image quality reduction.

Similar minor effects may be present when using star diagonals, as light travels through a multitude of lenses that increase or decrease effective focal length. The quality of the image generally depends on the quality of the optics (lenses) and viewing conditions—not on magnification.

Magnification itself is limited by optical characteristics. With any telescope or microscope, beyond a practical maximum magnification, the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is sometimes called empty magnification.

To get the most detail out of a telescope, it is critical to choose the right magnification for the object being observed. Some objects appear best at low power, some at high power, and many at a moderate magnification. There are two values for magnification, a minimum and maximum. A wider field of view eyepiece may be used to keep the same eyepiece focal length whilst providing the same magnification through the telescope. For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by diffraction.

Visual
The visual magnification $$M$$ of the field of view through a telescope can be determined by the telescope's focal length $$f$$ divided by the eyepiece focal length $$f_{e}$$ (or diameter). The maximum is limited by the focal length of the eyepiece.

An example of visual magnification using a telescope with a 1200 mm focal length and 3 mm eyepiece is given by: $$M = \frac {f}{f_{e}} = \frac {1200}{3} = 400$$

Minimum
There are two issues constraining the lowest useful magnification on a telescope:
 * The light beam exiting the eyepiece needs to be small enough to enter the pupil of the observer's eye. If the cylinder of light emerging from they eyepiece is too wide to enter the observer's eye, some of the light gathered by the telescope will be wasted, and the image seen will be dimmer and less clear than it would be at a higher magnification.
 * For telescope designs with obstructions in the light path (e.g. most catadioptric telescopes, but not spyglass-style refracting telescopes) the magnification must be high enough to keep the central obstruction out of focus, to prevent it from coming into view as a central "black spot". Both of these issues depend on the size of the pupil of the observer's eye, which will be narrower in daylight and wider in the dark.

Both constraints boil down to approximately the same rule: The magnification of the viewed image, $$\ M\ ,$$ must be high enough to make the eyepiece exit pupil, $$\ d_\mathsf{ep}\ ,$$ no larger than the pupil of the observer's own eye. The formula for the eypiece exit pupil is
 * $$\ d_\mathsf{ep} = \frac{\ D\ }{\ M\ } \ $$

where $$\ D\ $$ is the light-collecting diameter of the telescope's aperture.

Dark-adapted pupil sizes range from 8–9 mm for young children, to a "normal" or standard value of 7 mm for most adults aged 30–40, to 5–6 mm for retirees in their 60s and 70s. A lifetime spent exposed to chronically bright ambient light, such as sunlight reflected off of open fields of snow, or white-sand beaches, or cement, will tend to make individuals' pupils permanently smaller. Sunglasses greatly help, but once shrunk by long-time over-exposure to bright light, even the use of opthamalogic drugs cannot restore lost pupil size. Most observers' eyes instantly respond to darkness by widening the pupil to almost its maximum, although complete adaption to night vision generally takes at least a half-hour. (There is usually a slight extra widening of the pupil the longer the pupil remains dilated / relaxed.) The improvement in brightness with reduced magnification has a limit related to something called the exit pupil. The exit pupil is the cylinder of light exiting the eyepiece and entering the pupil of the eye; hence the lower the magnification, the larger the exit pupil. It is the image of the shrunken sky-viewing aperture of the telescope, reduced by the magnification factor, $$\ M\ ,$$ of the eyepiece-telescope combination:
 * $$\ M = \frac{\ L\ }{ \ell }\ ,$$

where $$\ L\ $$ is the focal length of the telescope and $$\ \ell\ $$ is the focal length of the eyepiece.

Ideally, the exit pupil of the eyepiece, $$\ d_\mathsf{ep}\ ,$$ matches the pupil of the observer's eye: If the exit pupil from the eyepiece is larger than the pupil of individual observer's eye, some of the light delivered from the telescope will be cut off. If the eyepiece exit pupil is the same or smaller than the pupil of the observer's eye, then all of the light collected by the telescope aperture will enter the eye, with lower magnification producing a brighter image, as long as all of the captured light gets into the eye.

The minimum $$\ M_\mathsf{min}\ $$ can be calculated by dividing the telescope aperture $$\ D\ $$ over the largest tolerated exit pupil diameter $$\ d_\mathsf{ep} ~.$$
 * $$\ M_\mathsf{min} = \frac{\ D\ }{\ d_\mathsf{ep} } \ $$

Decreasing the magnification past this limit will not increase brightness nor improve clarity: Beyond this limit there is no benefit from lower magnification. Likewise calculating the exit pupil $$\ d_\mathsf{ep}\ $$ is a division of the aperture diameter $$\ D\ $$ and the visual magnification $$\ M\ $$ used. The minimum often may not be reachable with some telescopes, a telescope with a very long focal length may require a longer focal length eyepiece than is available.

An example of the lowest usable magnification using a fairly common 10″ (254 mm) aperture and the standard adult 7 mm maximum exit pupil is given by: $$\ M_\mathsf{min} = \frac{ D }{\ d_\mathsf{ep} } = \frac{\ 254\ }{ 7 } \approx 36\!\times ~.$$ If the telescope happened to have a 1 200  mm focal length ($$\ L\ $$), the longest recommended eyepiece focal length ($$\ \ell\ $$) would be $$\ \ell = \frac{\ L\ }{ M } \approx \frac{\ 1\ 200\mathsf{\ mm\ } }{ 36 } \approx 33\mathsf{\ mm} ~.$$ An eyepiece of the same apparent field-of-view but longer focal-length will deliver a wider true field of view, but dimmer image. If the telescope has a central obstruction (e.g. a Newtonian, Maksutov, or Schmidt–Cassegrain telescope) it is also likely that the low magnification will make the obstruction come into focus enough to make a black spot in the middle of the image.

Calculating in the other direction, the exit pupil diameter of a 254 mm telescope aperture at 60× magnification is given by: $$\ d_\mathsf{ep} = \frac{\ D\ }{ M } = \frac{\ 254\ }{ 60 } \approx 4.2\mathsf{\ mm\ } ,$$ well within pupil size of dark-adapted eyes of observers of almost all ages. Assuming the same telescope focal length as above, the eyepiece focal length that would produce a 60× magnification is $$\ \ell = \frac{\ L\ }{ M } = \frac{\ 1\ 200\mathsf{\ mm\ } }{ 60 } \approx 20\mathsf{\ mm} ~.$$

Optimum
The following are rules-of-thumb for useful magnifications appropriate to different type objects:
 * For small objects with low surface brightness (such as galaxies), use a moderate magnification.
 * For small objects with moderate surface brightness (such as planetary nebulae), use a high magnification.
 * For small objects with high surface brightness (such as planets), use the highest magnification that the current night's "seeing" will allow, and consider adding in astronomical filters to sharpen the image.
 * For large objects (such as the Andromeda galaxy or wide-field diffuse nebulae), regardless of surface brightness use low magnification, often in the range of minimum magnification.
 * For very to extremely bright, large objects (the Moon and the Sun) narrow-down the aperture of the telescope by covering it with a piece of cardboard with a small hole in it, and insert filters as-needed to both cut down excess brightness and to enhance the contrast of surface features.

Only personal experience determines the best optimum magnifications for objects, relying on observational skills and seeing conditions, and the status of the pupil of observer's eye at the moment (e.g. a lower magnification may be required if there is enough moonlight to prevent complete dark adaption).

Field of view
Field of view is the extent of the observable world seen at any given moment, through an instrument (e.g., telescope or binoculars), or by naked eye. There are various expressions of field of view, being a specification of an eyepiece or a characteristic determined from an eyepiece and telescope combination. A physical limit derives from the combination where the FOV cannot be viewed larger than a defined maximum, due to diffraction of the optics.

Apparent
Apparent field of view (commonly referred to as AFOV) is the perceived angular size of the field stop of the eyepiece, typically measured in degrees. It is a fixed property of the eyepiece's optical design, with common commercially available eyepieces offering a range of apparent fields from 40° to 120°. The apparent field of view of an eyepiece is limited by a combination of the eyepiece's field stop diameter, and focal length, and is independent of magnification used.

In an eyepiece with a very wide apparent field of view, the observer may perceive that the view through the telescope stretches out to their peripheral vision, giving a sensation that they are no longer looking through an eyepiece, or that they are closer to the subject of interest than they really are. In contrast, an eyepiece with a narrow apparent field of view may give the sensation of looking through a tunnel or small porthole window, with the black field stop of the eyepiece occupying most of the observer's vision.

A wider apparent field of view permits the observer to see more of the subject of interest (that is, a wider true field of view) without reducing magnification to do so. However, the relationship between true field of view, apparent field of view, and magnification is not direct, due to increasing distortion characteristics that correlate with wider apparent fields of view. Instead, both true field of view and apparent field of view are consequences of the eyepiece's field stop diameter.

Apparent field of view differs from true field of view in so far as true field of view varies with magnification, whereas apparent field of view does not. The wider field stop of a wide angle eyepiece permits the viewing of a wider section of the real image formed at the telescope's focal plane, thus impacting the calculated true field of view.

An eyepiece's apparent field of view can influence total view brightness as perceived by the eye, since the apparent angular size of the field stop will determine how much of the observer's retina is illuminated by the exit pupil formed by the eyepiece. However, apparent field of view has no impact on the apparent surface brightness (that is, brightness per unit area) of objects contained within the field of view.

True
True FOV is the width of what is actually seen through any given eyepiece / telescope combination.

There are two formulae for calculating true field of view:

 * 1) Apparent field of view method given by $$v_{t} = \frac {v_{a}}{M}$$,  where $$v_{t}$$ is the true FOV, $$v_{a}$$ is the apparent field of view of the eyepiece, and $$M$$ is the magnification being used.
 * 2) Eyepiece field stop method given by $$v_{t} = \frac {d_f}{f_t} \times 57.3$$, where $$v_{t}$$ is the true FOV, $$d_{f}$$ is the eyepiece field stop diameter in millimeters and $$f_{t}$$ is the focal length of the telescope in millimeters.

The eyepiece field stop method is more accurate than the apparent field of view method, however not all eyepieces have an easily knowable field stop diameter.

Maximum
Max FOV is the maximum useful true field of view limited by the optics of the telescope. It is a physical limitation where increases beyond the maximum remain at maximum. Max FOV $$v_{m}$$ is the barrel size $$B$$ over the telescope's focal length $$f$$ converted from radian to degrees.

An example of max FOV using a telescope with a barrel size of 31.75 mm (1.25 inches) and focal length of 1200 mm is given by: $$v_{m} = B \cdot \frac {\frac {180}{\pi}}{f} \approx 31.75 \cdot \frac {57.2958}{1200} \approx 1.52^\circ$$

Observing through a telescope
There are many properties of optical telescopes and the complexity of observation using one can be a daunting task; experience and experimentation are the major contributors to understanding how to maximize one's observations. In practice, only two main properties of a telescope determine how observation differs: the focal length and aperture. These relate as to how the optical system views an object or range and how much light is gathered through an ocular eyepiece. Eyepieces further determine how the field of view and magnification of the observable world change.

Observable world
The observable world is what can be seen using a telescope. When viewing an object or range, the observer may use many different techniques. Understanding what can be viewed and how to view it depends on the field of view. Viewing an object at a size that fits entirely in the field of view is measured using the two telescope properties—focal length and aperture, with the inclusion of an ocular eyepiece with suitable focal length (or diameter). Comparing the observable world and the angular diameter of an object shows how much of the object we see. However, the relationship with the optical system may not result in high surface brightness. Celestial objects are often dim because of their vast distance, and detail may be limited by diffraction or unsuitable optical properties.

Field of view and magnification relationship
Finding what can be seen through the optical system begins with the eyepiece providing the field of view and magnification; the magnification is given by the division of the telescope and eyepiece focal lengths. Using an example of an amateur telescope such as a Newtonian telescope with an aperture $$D$$ of 130 mm (5") and focal length $$f$$ of 650 mm (25.5 inches), one uses an eyepiece with a focal length $$d$$ of 8 mm and apparent FOV $$v_{a}$$ of 52°. The magnification at which the observable world is viewed is given by: $$M = \frac {f}{d} = \frac {650}{8} = 81.25$$. The field of view $$v_{t}$$ requires the magnification, which is formulated by its division over the apparent field of view: $$v_{t} = \frac {v_{a}}{M} = \frac {52}{81.25} = 0.64$$. The resulting true field of view is 0.64°, not allowing an object such as the Orion nebula, which appears elliptical with an angular diameter of 65 × 60 arcminutes, to be viewable through the telescope in its entirety, where the whole of the nebula is within the observable world. Using methods such as this can greatly increase one's viewing potential ensuring the observable world can contain the entire object, or whether to increase or decrease magnification viewing the object in a different aspect.

Brightness factor
The surface brightness at such a magnification significantly reduces, resulting in a far dimmer appearance. A dimmer appearance results in less visual detail of the object. Details such as matter, rings, spiral arms, and gases may be completely hidden from the observer, giving a far less complete view of the object or range. Physics dictates that at the theoretical minimum magnification of the telescope, the surface brightness is at 100%. Practically, however, various factors prevent 100% brightness; these include telescope limitations (focal length, eyepiece focal length, etc.) and the age of the observer.

Age plays a role in brightness, as a contributing factor is the observer's pupil. With age the pupil naturally shrinks in diameter; generally accepted a young adult may have a 7 mm diameter pupil, an older adult as little as 5 mm, and a younger person larger at 9 mm. The minimum magnification $$m$$ can be expressed as the division of the aperture $$D$$ and pupil $$p$$ diameter given by: $$m = \frac {D}{d} = \frac {130}{7} \approx 18.6$$. A problematic instance may be apparent, achieving a theoretical surface brightness of 100%, as the required effective focal length of the optical system may require an eyepiece with too large a diameter.

Some telescopes cannot achieve the theoretical surface brightness of 100%, while some telescopes can achieve it using a very small-diameter eyepiece. To find what eyepiece is required to get minimum magnification one can rearrange the magnification formula, where it is now the division of the telescope's focal length over the minimum magnification: $$ \frac {F}{m} = \frac {650}{18.6} \approx 35$$. An eyepiece of 35 mm is a non-standard size and would not be purchasable; in this scenario to achieve 100% one would require a standard manufactured eyepiece size of 40 mm. As the eyepiece has a larger focal length than the minimum magnification, an abundance of wasted light is not received through the eyes.

Exit pupil
The limit to the increase in surface brightness as one reduces magnification is the exit pupil: a cylinder of light that projects out the eyepiece to the observer. An exit pupil must match or be smaller in diameter than one's pupil to receive the full amount of projected light; a larger exit pupil results in the wasted light. The exit pupil $$e$$ can be derived with from division of the telescope aperture $$D$$ and the minimum magnification $$m$$, derived by: $$e = \frac {D}{m} = \frac {130}{18.6} \approx 7$$. The pupil and exit pupil are almost identical in diameter, giving no wasted observable light with the optical system. A 7 mm pupil falls slightly short of 100% brightness, where the surface brightness $$B$$ can be measured from the product of the constant 2, by the square of the pupil $$p$$ resulting in: $$B = 2*p^2 = 2*7^2 = 98$$. The limitation here is the pupil diameter; it is an unfortunate result and degrades with age. Some observable light loss is expected and decreasing the magnification cannot increase surface brightness once the system has reached its minimum usable magnification, hence why the term is referred to as usable.

Image Scale
When using a CCD to record observations, the CCD is placed in the focal plane. Image scale (sometimes called plate scale) is how the angular size of the object being observed is related to the physical size of the projected image in the focal plane

$$i = \frac{\alpha}{s},$$

where $$i$$ is the image scale, $$\alpha$$ is the angular size of the observed object, and $$s$$ is the physical size of the projected image. In terms of focal length image scale is

$$i = \frac{1}{f},$$

where $$i$$ is measured in radians per meter (rad/m), and $$f$$ is measured in meters. Normally $$i$$ is given in units of arcseconds per millimeter ("/mm). So if the focal length is measured in millimeters, the image scale is

$$i\ (''/\mathrm{mm}) = \frac{1}{f\ (\mathrm{mm})}\left[\frac{180 \times 3600}{\pi}\right].$$

The derivation of this equation is fairly straightforward and the result is the same for reflecting or refracting telescopes. However, conceptually it is easier to derive by considering a reflecting telescope. If an extended object with angular size $$\alpha$$ is observed through a telescope, then due to the Laws of reflection and Trigonometry the size of the image projected onto the focal plane will be

$$s = \tan(\alpha) f.$$

The image scale (angular size of object divided by size of projected image) will be

$$i = \frac{\alpha}{s} = \frac{\alpha}{\tan(\alpha) f},$$

and by using the small angle relation $$\tan(a) \approx a$$, when $$a \ll 1$$ (N.B. only valid if $$a$$ is in radians), we obtain

$$i = \frac{\alpha}{\alpha f} = \frac{1}{f}.$$

Imperfect images
No telescope can form a perfect image. Even if a reflecting telescope could have a perfect mirror, or a refracting telescope could have a perfect lens, the effects of aperture diffraction are unavoidable. In reality, perfect mirrors and perfect lenses do not exist, so image aberrations in addition to aperture diffraction must be taken into account. Image aberrations can be broken down into two main classes, monochromatic, and polychromatic. In 1857, Philipp Ludwig von Seidel (1821–1896) decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.

The five Seidel aberrations

 * Spherical aberration : The difference in focal length between paraxial rays and marginal rays, proportional to the square of the objective diameter.
 * Coma : A defect by which points appear as comet-like asymmetrical patches of light with tails, which makes measurement very imprecise. Its magnitude is usually deduced from the optical sine theorem.
 * Astigmatism : The image of a point forms focal lines at the sagittal and tangental foci and in between (in the absence of coma) an elliptical shape.
 * Petzval field curvature: The Petzval field curvature means that the image, instead of lying in a plane, actually lies on a curved surface, described as hollow or round. This causes problems when a flat imaging device is used e.g., a photographic plate or CCD image sensor.
 * Distortion: Either barrel or pincushion, a radial distortion that must be corrected when combining multiple images (similar to stitching multiple photos into a panoramic photo).

Optical defects are always listed in the above order, since this expresses their interdependence as first order aberrations via moves of the exit/entrance pupils. The first Seidel aberration, Spherical Aberration, is independent of the position of the exit pupil (as it is the same for axial and extra-axial pencils). The second, coma, changes as a function of pupil distance and spherical aberration, hence the well-known result that it is impossible to correct the coma in a lens free of spherical aberration by simply moving the pupil. Similar dependencies affect the remaining aberrations in the list.

Chromatic aberrations

 * Longitudinal chromatic aberration: As with spherical aberration this is the same for axial and oblique pencils.
 * Transverse chromatic aberration (chromatic aberration of magnification)

Astronomical research telescopes
Optical telescopes have been used in astronomical research since the time of their invention in the early 17th century. Many types have been constructed over the years depending on the optical technology, such as refracting and reflecting, the nature of the light or object being imaged, and even where they are placed, such as space telescopes. Some are classified by the task they perform such as solar telescopes.

Large reflectors
Nearly all large research-grade astronomical telescopes are reflectors. Some reasons are:
 * In a lens the entire volume of material has to be free of imperfection and inhomogeneities, whereas in a mirror, only one surface has to be perfectly polished.
 * Light of different colors travels through a medium other than vacuum at different speeds. This causes chromatic aberration.
 * Reflectors work in a wider spectrum of light since certain wavelengths are absorbed when passing through glass elements like those found in a refractor or catadioptric.
 * There are technical difficulties involved in manufacturing and manipulating large-diameter lenses. One of them is that all real materials sag in gravity. A lens can only be held by its perimeter. A mirror, on the other hand, can be supported by the whole side opposite to its reflecting face.

Most large research reflectors operate at different focal planes, depending on the type and size of the instrument being used. These including the prime focus of the main mirror, the cassegrain focus (light bounced back down behind the primary mirror), and even external to the telescope all together (such as the Nasmyth and coudé focus).

A new era of telescope making was inaugurated by the Multiple Mirror Telescope (MMT), with a mirror composed of six segments synthesizing a mirror of 4.5 meters diameter. This has now been replaced by a single 6.5 m mirror. Its example was followed by the Keck telescopes with 10 m segmented mirrors.

The largest current ground-based telescopes have a primary mirror of between 6 and 11 meters in diameter. In this generation of telescopes, the mirror is usually very thin, and is kept in an optimal shape by an array of actuators (see active optics). This technology has driven new designs for future telescopes with diameters of 30, 50 and even 100 meters.

Relatively cheap, mass-produced ~2 meter telescopes have recently been developed and have made a significant impact on astronomy research. These allow many astronomical targets to be monitored continuously, and for large areas of sky to be surveyed. Many are robotic telescopes, computer controlled over the internet (see e.g. the Liverpool Telescope and the Faulkes Telescope North and South), allowing automated follow-up of astronomical events.

Initially the detector used in telescopes was the human eye. Later, the sensitized photographic plate took its place, and the spectrograph was introduced, allowing the gathering of spectral information. After the photographic plate, successive generations of electronic detectors, such as the charge-coupled device (CCDs), have been perfected, each with more sensitivity and resolution, and often with a wider wavelength coverage.

Current research telescopes have several instruments to choose from such as:
 * imagers, of different spectral responses
 * spectrographs, useful in different regions of the spectrum
 * polarimeters, that detect light polarization.

The phenomenon of optical diffraction sets a limit to the resolution and image quality that a telescope can achieve, which is the effective area of the Airy disc, which limits how close two such discs can be placed. This absolute limit is called the diffraction limit (and may be approximated by the Rayleigh criterion, Dawes limit or Sparrow's resolution limit). This limit depends on the wavelength of the studied light (so that the limit for red light comes much earlier than the limit for blue light) and on the diameter of the telescope mirror. This means that a telescope with a certain mirror diameter can theoretically resolve up to a certain limit at a certain wavelength. For conventional telescopes on Earth, the diffraction limit is not relevant for telescopes bigger than about 10 cm. Instead, the seeing, or blur caused by the atmosphere, sets the resolution limit. But in space, or if adaptive optics are used, then reaching the diffraction limit is sometimes possible. At this point, if greater resolution is needed at that wavelength, a wider mirror has to be built or aperture synthesis performed using an array of nearby telescopes.

In recent years, a number of technologies to overcome the distortions caused by atmosphere on ground-based telescopes have been developed, with good results. See adaptive optics, speckle imaging and optical interferometry.

title: Optical telescope


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Ernest Augustus, King of Hanover

Ernest Augustus (Ernst August; 5 June 1771 – 18 November 1851) was King of Hanover from 20 June 1837 until his death in 1851. As the fifth son of George III of the United Kingdom and Hanover, he initially seemed unlikely to become a monarch, but none of his elder brothers had a legitimate son. When his elder brother William IV, who ruled both kingdoms, died in 1837, his niece Victoria inherited the British throne under British succession law, while Ernest succeeded in Hanover under Salic law, which barred women from the succession, thus ending the personal union between Britain and Hanover that had begun in 1714.

Ernest was born in London but was sent to Hanover in his adolescence for his education and military training. While serving with Hanoverian forces near Tournai against Revolutionary France, he received a disfiguring facial wound. He was created Duke of Cumberland and Teviotdale in 1799. Although his mother, Queen Charlotte, disapproved of his marriage in 1815 to her twice-widowed niece, Frederica of Mecklenburg-Strelitz, it proved happy. The eldest son of George III, the Prince of Wales (later George IV), had one child, Charlotte, who was expected to become the British queen, but she died in 1817, giving Ernest some prospect of succeeding to the British and Hanoverian thrones. However, his elder brother Prince Edward, Duke of Kent and Strathearn, fathered the eventual British heir, Victoria, in 1819 shortly before the birth of Ernest's only child, George.

Ernest was an active member of the House of Lords, where he maintained an extremely conservative record. There were persistent allegations (reportedly spread by his political foes) that he had murdered his valet, had fathered a son by his sister Sophia, and intended to take the British throne by murdering Victoria. Following the death of William IV, Ernest became Hanover's first resident ruler since George I. He had a generally successful fourteen-year reign but excited controversy near its start when he voided the liberal constitution granted before his reign and dismissed the Göttingen Seven, including the Brothers Grimm, from their professorial positions for protesting against this decision. In 1848, the King put down an attempted revolution. Hanover joined the German customs union in 1850 despite Ernest's reluctance. Ernest died the next year and was succeeded by his son, George V.

Early life (1771–1799)
Ernest Augustus, the fifth son of King George III and Queen Charlotte, was born at Buckingham House, London, on 5 June 1771, and baptised on 1 July 1771 at St James's Palace. His sponsors were Duke Ernest of Mecklenburg (his maternal uncle), Duke Moritz of Saxe-Gotha (his paternal great-uncle, for whom the Earl of Hertford stood proxy), and the Hereditary Princess of Hesse-Kassel (his father's cousin, for whom the Countess of Egremont stood proxy). After leaving the nursery, he lived with his two younger brothers, Prince Adolphus (later Duke of Cambridge) and Prince Augustus (later Duke of Sussex), and a tutor in a house on Kew Green, near his parents' residence at Kew Palace. Though the King never left England in his life, he sent his younger sons to Germany in their adolescence. According to the historian John Van der Kiste, this was done to limit the influence Ernest's eldest brother George, Prince of Wales, who was leading an extravagant lifestyle, would have over his younger brothers. At the age of fifteen, Prince Ernest and his two younger brothers were sent to the University of Göttingen, located in his father's domain of Hanover. Ernest proved a keen student and after being tutored privately for a year, while learning German, he attended lectures at the university. Though King George ordered that the princes' household be run along military lines and that they follow the university's rules, the merchants of the Electorate proved willing to extend credit to the princes and all three fell into debt.

In 1790, Ernest asked his father for permission to train with Prussian forces. Instead, in January 1791, he and Prince Adolphus were sent to Hanover to receive military training under the supervision of Field Marshal Wilhelm von Freytag. Before leaving Göttingen, Ernest penned a formal letter of thanks to the university and wrote to his father, "I should be one of the most ungrateful of men if ever I was forgetful of all I owe to Göttingen & its professors."

As a lieutenant, Ernest learned cavalry drill and tactics under Captain von Linsingen of the Queen's Light Dragoons and proved to be an excellent horseman, as well as a good shot. After only two months of training, Freytag was so impressed by the prince's progress that he gave him a place in the cavalry as captain. Ernest was supposed to receive infantry training, but the King, also impressed by his son's prowess, allowed him to remain with the cavalry.

In March 1792, the King commissioned Prince Ernest Augustus as a colonel into the 9th Hanoverian Light Dragoons. The prince served in the Low Countries in the War of the First Coalition, under his elder brother Prince Frederick, Duke of York, then commander of the combined British, Hanoverian and Austrian forces. Seeing action near the Walloon town of Tournai in August 1793, he sustained a sabre wound to the head, which resulted in a disfiguring scar. During the Battle of Tourcoing in northern France on 18 May 1794, his left arm was injured by a cannonball which passed close by him. In the days after the battle, the sight in his left eye faded. In June, he was sent to Britain to convalesce, his first stay there since 1786. Ernest resumed his duties in early November, by now promoted to major-general. He hoped his new rank would bring him a corps or brigade command, but none was forthcoming as the Allied armies retreated slowly through the Netherlands towards Germany. By February 1795, they had reached Hanover. Ernest remained in Hanover over the next year, holding several unimportant postings. He had requested a return home to seek treatment for his eye, but it was not until early 1796 that the King agreed and allowed Ernest to return to Britain. There, Prince Ernest consulted a notable eye doctor, Wathen Waller, but Waller apparently found his condition inoperable, as no operation took place. Once back in Britain, Ernest repeatedly sought to be allowed to join the British forces on the Continent, even threatening to join the Yeomanry as a private, but both the King and the Duke of York refused him permission. Ernest did not want to rejoin the Hanoverian forces, as they were not then involved in the fighting. In addition, Freytag was seriously ill and Ernest was unwilling to serve under his likely successor, Count von Wallmoden.

Military commander
On 23 April 1799, George III created Prince Ernest Augustus Duke of Cumberland and Teviotdale and Earl of Armagh, and Ernest was granted an allowance of £12,000 a year, equivalent to £ in. Though he was made a lieutenant-general, of both British and Hanoverian forces, he remained in England and, with a seat in the House of Lords, entered politics. Ernest had extreme Tory views and soon became a leader of the right wing of the party. King George had feared that Ernest, like some of his elder brothers, would display Whig tendencies. Reassured on that point, in 1801, the King had Ernest conduct the negotiations which led to the formation of the Addington government. In February 1802, King George granted his son the colonelcy of the 27th Light Dragoons, a post which offered the option of transfer to the colonelcy of the 15th Light Dragoons when a vacancy arose. A vacancy promptly occurred and the Duke became the colonel of the 15th Light Dragoons in March 1802. Although the post could have been a sinecure, Ernest involved himself in the affairs of the regiment and led it on manoeuvres.

In early 1803, the Duke of York appointed Ernest as commander of the Severn District, in charge of the forces in and around the Severn Estuary. When war with France broke out again after the Peace of Amiens, Frederick appointed Ernest to the more important Southwest District, comprising Hampshire, Dorset and Wiltshire. Though Ernest would have preferred command of the King's German Legion, composed mostly of expatriates from French-occupied Hanover, he accepted the post. The Duke of Cumberland increased the defences on the South Coast, especially around the town of Weymouth, where his father often spent time in the summer.

The Acts of Union 1800 had given Ireland representation in Parliament, but existing law prevented Irish Catholics from serving there because of their religion. "Catholic emancipation" was a major political issue of the first years of the 19th century. The Duke of Cumberland was a strong opponent of giving political rights to Catholics, believing that emancipation would be a violation of the King's Coronation Oath to uphold Anglicanism and spoke out in the House of Lords against emancipation. Protestant Irish organisations supported the Duke; he was elected Chancellor of the University of Dublin in 1805 and Grand Master of the Orange Lodges two years later.

The Duke repeatedly sought a post with Allied forces fighting against France, but was sent to the Continent only as an observer. In 1807, he advocated sending British troops to join the Prussians and Swedes in attacking the French at Stralsund (today, in northeastern Germany). The Grenville government refused to send forces. Shortly afterwards, the government fell and the new prime minister, the Duke of Portland, agreed to send Ernest with 20,000 troops. However, they were sent too late: the French defeated Prussia and Sweden at the Battle of Stralsund before Ernest and his forces could reach the town. Ernest was promoted to full general of the army in 1808, backdated to 1805.

Sellis incident and Weymouth controversy
In the early hours of 31 May 1810, Ernest, by his written account, was struck in the head several times while asleep in bed, awakening him. He ran for the door, where he was wounded in the leg by a sabre. He called for help and one of his valets, Cornelius Neale, responded and aided him. Neale raised the alarm and the household soon realised that Ernest's other valet, Joseph Sellis, was not among them and that the door to Sellis's room was locked. The lock was forced and Sellis was discovered with his throat freshly cut, a wound apparently self-inflicted. Ernest received several serious wounds during the apparent attack and required over a month to recover from his injuries. The social reformer and anti-monarchist Francis Place managed to join the inquest jury and became its foreman. Place went to the office of a barrister friend to study inquest law and aggressively questioned witnesses. Place also insisted that the inquest be opened to the public and press, and so cowed the coroner that he basically ran the inquest himself. Nevertheless, the jury returned a unanimous verdict of suicide against Sellis.

Much of the public blamed Ernest for Sellis's death. The more extreme Whig papers, anti-royal pamphleteers, and caricaturists all offered nefarious explanations for Sellis's death, in which the Duke was to blame. Some stories had the Duke cuckolding Sellis, with the attack as retaliation, or Sellis killed for finding Ernest and Mrs. Sellis in bed together. Others suggested that the Duke was the lover of either Sellis or Neale, and that blackmail had played a part in the death. Both Roger Fulford and John Van der Kiste, who wrote books about George III's children, ascribe part of the animus and fear towards the Duke to the fact that he did not conduct love affairs in public, as did his elder brothers. According to them, the public feared what vices might be going on behind the locked doors of the Duke's house and assumed the worst.

In early 1813, Ernest was involved in political scandal during an election contest in Weymouth following the general election the previous year. The Duke was shown to be one of three trustees who were able to dictate who would represent Weymouth in Parliament. It being considered improper for a peer to interfere in an election to the House of Commons, there was considerable controversy and the government sent Ernest to Europe as an observer to accompany Hanoverian troops, which were again engaged in war against France. Though he saw no action, Ernest was present at the Battle of Leipzig, a major victory for the Allies. Following this, Ernest received ultimate promotion, to Field Marshal, on 26 November 1813.

Marriage
Ernest met and fell in love in mid-1813 with his first cousin, Duchess Frederica of Mecklenburg-Strelitz, wife of Prince Frederick William of Solms-Braunfels and widow of Prince Louis of Prussia. The two agreed to wed if Frederica became free to marry. Her marriage to Frederick William had not been a success; her husband, seeing the marriage was beyond hope, agreed to a divorce, but his sudden death in 1814 removed the necessity. Some considered the death too convenient and suspected Frederica of poisoning her husband. Queen Charlotte opposed the marriage: before Frederica had married Frederick William, she had jilted Ernest's younger brother, Prince Adolphus, Duke of Cambridge, after the engagement was announced.

Following the marriage in Germany on 29 May 1815, Queen Charlotte refused to receive her new daughter-in-law, nor would the Queen attend the resolemnisation of the Cumberlands' marriage at Kew, which Ernest's four elder brothers attended. The Prince of Wales (who had been Prince Regent since 1811) found the Cumberlands' presence in Britain embarrassing, and offered him money and the governorship of Hanover if they would leave for the Continent. Ernest refused and the Cumberlands divided their time between Kew and St. James's Palace for the next three years. The Queen remained obstinate in her refusal to receive Frederica. Despite these family troubles, the Cumberlands had a happy marriage. The government of Lord Liverpool asked Parliament to increase the Duke's allowance by £6,000 per year in 1815 (equal to about £0 today), so he could meet increased expenses due to his marriage. The Duke's involvement in the Weymouth election became an issue and the bill failed by one vote. Liverpool tried again in 1817; this time the bill failed by seven votes.

At the time of the Duke's marriage in 1815, it seemed to have little dynastic significance to Britain. Princess Charlotte of Wales, only child of the Prince Regent, was the King's only legitimate grandchild. The young princess was expected to have children who would secure the British succession, especially after she married Prince Leopold of Saxe-Coburg-Saalfeld in 1816. Both the Prince Regent and the Duke of York were married but estranged from their wives, while the next two brothers, Prince William, Duke of Clarence, and Prince Edward, Duke of Kent and Strathearn, were unmarried. On 6 November 1817, Princess Charlotte died after delivering a stillborn son. King George was left with twelve surviving children and no surviving legitimate grandchildren. Most of the unmarried royal dukes hurriedly sought out suitable brides and hastened to the altar, hoping to secure the succession for another generation.

Seeing little prospect of the Queen giving in and receiving her daughter-in-law, the Cumberlands moved to Germany in 1818. They had difficulty living within their means in Britain and the cost of living was much lower in Germany. Queen Charlotte died on 17 November 1818, but the Cumberlands remained in Germany, living principally in Berlin, where the Duchess had relatives. In 1817, the Duchess had a stillborn daughter; in 1819 she gave birth to a boy, Prince George of Cumberland. The Duke occasionally visited England, where he stayed with his eldest brother, who in 1820 succeeded to the British and Hanoverian thrones as George IV. George III's fourth son, the Duke of Kent, died six days before his father, but left a daughter, Princess Alexandrina Victoria of Kent. With the death of George III, Ernest became fourth in line to the British throne, following the Duke of York (who died without legitimate issue in 1827), the Duke of Clarence and Princess Alexandrina Victoria. Returning to England, his political power was again considerable, as it seemed possible that he would succeed to the throne.

Politics and unpopularity
In 1826, Parliament finally voted to increase Ernest's allowance. The Liverpool government argued that the Duke needed an increased allowance to pay for Prince George's education; even so, it was opposed by many Whigs. The bill, which passed the House of Commons 120–97, required George to live in England if Ernest was to receive the money.

In 1828, Ernest was staying with the King at Windsor Castle when severe disturbances broke out in Ireland among Catholics. The Duke was an ardent supporter of the Protestant cause in Ireland and returned to Berlin in August, believing that the government, led by the Duke of Wellington, would deal firmly with the Irish. In January 1829, the Wellington government announced that it would introduce a Catholic emancipation bill to conciliate the Irish. Disregarding a request from Wellington that he remain abroad, Ernest returned to London and was one of the leading opponents to the Roman Catholic Relief Act 1829, influencing George IV against the bill. Within days of his arrival, the King instructed the officers of his Household to vote against the bill. Hearing of this, Wellington told the King that he must resign as Prime Minister unless the King could assure him of complete support. The King initially accepted Wellington's resignation and Ernest attempted to put together a government united against Catholic emancipation. Though such a government would have had considerable support in the House of Lords, it would have had little support in the Commons and Ernest abandoned his attempt. The King recalled Wellington. The bill passed the Lords and became law.

The Wellington government hoped that Ernest would return to Germany, but he moved his wife and son to Britain in 1829. The Times reported that they would live at Windsor in the "Devil's Tower"; instead, the Duke reopened his house at Kew. They settled there as rumours flew that Thomas Garth, thought to be the illegitimate son of Ernest's sister Princess Sophia, had been fathered by Ernest. It was also said that Ernest had blackmailed the King by threatening to expose this secret, though Van der Kiste points out that Ernest would have been ill-advised to blackmail with a secret which, if exposed, would destroy him. These rumours were spread as Ernest journeyed to London to fight against Catholic emancipation. Whig politician and diarist Thomas Creevey wrote about the Garth rumour in mid-February and there is some indication the rumours began with Princess Lieven, wife of the Russian ambassador.

Newspapers also reported, in July 1829, that the Duke had been thrown out of Lord Lyndhurst's house for assaulting Lyndhurst's wife Sarah. In early 1830, a number of newspapers printed articles hinting that Ernest was having an affair with Lady Graves, a mother of fifteen, now past fifty. In February 1830, Lord Graves, Ernest's lord of the bedchamber and comptroller of his household, wrote a note to his wife expressing his confidence in her innocence, then cut his own throat. Two days after Lord Graves's death (and the day after the inquest), The Times printed an article connecting Lord Graves's death with Sellis's. After being shown the suicide note, The Times withdrew its implication there might be a connection between the two deaths. Nonetheless, many believed the Duke responsible for the suicide—or guilty of a second murder. The Duke later stated that he had been "accused of every crime in the decalogue". Ernest's biographer Anthony Bird states that while there is no proof, he has no doubt that the rumours against the Duke were spread by the Whigs for political ends. Another biographer, Geoffrey Willis, pointed out that no scandal had attached itself to the Duke during the period of over a decade when he resided in Germany; it was only when he announced his intention to return to Britain that "a campaign of unparalleled viciousness" began against him. The Duke of Wellington once told Charles Greville that George IV had said of Ernest's unpopularity, "there was never a father well with his son, or husband with his wife, or lover with his mistress, or a friend with his friend, that he did not try to make mischief between them." According to Bird, Ernest was the most unpopular man in England.

The Duke's influence at court was ended by the death of George IV in June 1830 and the succession of the Duke of Clarence as William IV. Wellington wrote that "the effect of the King's death will ... be to put an end to the Duke of Cumberland's political character and power in this country entirely". King William had no legitimate children (two daughters having died in infancy) and Ernest was now heir presumptive in Hanover, since the British heir presumptive, Princess Victoria, as a female could not inherit there. William realised that, so long as the Duke maintained a power base at Windsor, he could wield unwanted influence. The Duke was Gold Stick as head of the Household Cavalry; William made the Duke's post responsible to the Commander in Chief rather than to the King, and an insulted Ernest, outraged at the thought of having to report to an officer junior to himself, resigned.

King William again emerged triumphant when the new queen, Adelaide of Saxe-Meiningen, wished to quarter her horses in the stables customarily used by the consort, but which were then occupied by Ernest's horses. Ernest initially refused the King's order to remove the horses, but gave in when told that William's grooms would remove them if Ernest did not move them voluntarily. However, Ernest and William remained friendly throughout the latter's seven-year reign. Ernest's house at Kew was too small for his family; the King gave the Duke and Duchess lifetime residence in a nearby, larger house by the entrance to Kew Gardens. Ernest, who was against the extension of civil and religious liberties, opposed the Reform Act 1832 and was one of the "diehard" peers who voted against the bill on its final reading in which most Tories abstained under threat of seeing the House of Lords flooded with Whig peers. His unpopularity was deepened by the suggestion that he favoured the creation of Orange lodges in the army.

Ernest was the subject of more allegations in 1832, when two young women accused him of trying to ride them down as they walked near Hammersmith. The Duke had not left his grounds at Kew on the day in question and was able to ascertain that the rider was one of his equerries, who professed not to have seen the women. Nevertheless, newspapers continued to print references to the incident, suggesting that Ernest had done what the women stated and was cravenly trying to push blame on another. The same year, the Duke sued for libel after a book appeared accusing him of having his valet Neale kill Sellis and the jury found against the author. The Cumberlands suffered further tragedy, as young Prince George went blind. The prince had been blind in one eye for several years; an accident at age thirteen took the sight of the other. Ernest had hoped that his son might marry Princess Victoria and keep the British and Hanoverian thrones united, but the handicap made it unlikely that George could win Victoria's hand and raised questions about whether he should succeed in Hanover.

The Duke spent William IV's reign in the House of Lords, where he was assiduous in his attendance. Newspaper editor James Grant wrote that "He is literally—the door-keeper of course excepted—the first man in the House and the last out of it. And this not merely generally, but every night." Grant, in his observations of the leading members of the House of Lords, indicated that the Duke was not noted for his oratory (he delivered no speech longer than five minutes) and had a voice that was difficult to understand, though "his manner is most mild and conciliatory". Grant denigrated the Duke's intellect and influence, but stated that the Duke had indirect influence over several members, and that "he is by no means so bad a tactician as his opponents suppose".

Controversy arose in 1836 over the Orange Lodges. The lodges (which took anti-Catholic views) were said to be ready to rise and try to put the Duke of Cumberland on the throne on the death of King William. According to Joseph Hume, speaking in the House of Commons, Victoria was to be passed over on the grounds of her age, sex, and incapacity. The Commons passed a resolution calling for the dissolution of the lodges. When the matter reached the Lords, the Duke defended himself, saying of Princess Victoria, "I would shed the last drop of my blood for my niece." The Duke indicated that the Orange Lodge members were loyal and were willing to dissolve the lodges in Great Britain. According to Bird, this incident was the source of the widespread rumours that Ernest intended to murder Victoria and take the British throne for himself.

Constitutional controversy
On 20 June 1837, William IV died; Victoria succeeded him as Queen of the United Kingdom, while Ernest Augustus became King of Hanover. On 28 June 1837, Ernest entered his new domain, passing under a triumphal arch. For the first time in over a century, Hanover would have a ruler living there. Many Hanoverians were of a liberal perspective and would have preferred the popular viceroy, Prince Adolphus, Duke of Cambridge, to become king, but the Dukes of Sussex and Cambridge refused to lend themselves to any movement by which they would become king rather than their elder brother. According to Roger Fulford in his study of George III's younger sons, Royal Dukes, "In 1837, King Ernest was the only male descendant of George III who was willing and able to continue the connection with Hanover."

Hanover had received its first constitution, granted by the Prince Regent, in 1819; this did little more than denote Hanover's change from an electorate to a kingdom, guaranteed by the Congress of Vienna. The Duke of Cambridge, as King William's viceroy in Hanover, recommended a thorough reorganisation of the Hanoverian government. William IV had given his consent to a new constitution in 1833; the Duke of Cumberland's consent was neither asked nor received, and he had formally protested against the constitution's adoption without his consent. One provision of the constitution transferred the Hanoverian Domains (the equivalent of the British Crown Estate) from the sovereign to the state, eroding the monarch's power.

Immediately upon his arrival in Hanover, the King dissolved the Hanoverian Parliament, which had been convened under the disputed constitution. On 5 July, he proclaimed the suspension of the constitution, on the grounds that his consent had not been asked and that it did not meet the kingdom's needs. On 1 November 1837, the King issued a patent, declaring the constitution void, but upholding all laws passed under it. The 1819 constitution was restored. His son, Crown Prince George, endorsed the action.

In carrying the King's patent into effect, the Cabinet required all officeholders (including professors at Göttingen University) to renew their oaths of allegiance to the King. Seven professors (including the two Brothers Grimm) refused to take the oaths and agitated for others to protest against the King's decree. Since they did not take the oaths, the seven lost their positions and the King expelled the three most responsible (including Jacob Grimm) from Hanover. Only one of the seven, orientalist Heinrich Ewald, was a citizen of Hanover, and he was not expelled. In the final years of the King's reign, the three were invited to return. Ernest wrote of the incident to his brother-in-law, Frederick William III of Prussia, "If each of these seven gentlemen had addressed a letter to me expressing his opinion, I would have had no cause to take exception to their conduct. But to call a meeting and publish their opinions even before the government had received their protest—that is what they have done and that I cannot allow." Ernest received a deputation of Göttingen citizens who, fearing student unrest, applauded the dismissals. However, he was widely criticised in Europe, especially in Britain. In the British House of Commons, MP Colonel Thomas Perronet Thompson proposed to Parliament that if the as-yet-childless Queen Victoria died, making Ernest the British king, Parliament should declare that King Ernest had forfeited all rights to the British throne by his actions.

A more significant protest against the revocation of the 1833 constitution was the refusal of a number of towns to appoint parliamentary deputies. However, by 1840 a sufficient number of deputies had been appointed for the King to summon Parliament, which met for two weeks in August, approving a modified version of the 1819 constitution, passing a budget and sending a vote of thanks to the King. The Parliament met again the following year, passed a three-year budget and adjourned again.

National development and trade; 1848 crisis
At the time the King took the throne, the city of Hanover was a densely packed residential town and did not rise to the grand style of many German capitals. Once the political crises of the first years of his reign had subsided, he set out to remedy this state of affairs. Ernest's support led to gas lighting in the city streets of Hanover, up-to-date sanitation and the development of a new residential quarter. He had the plans altered in 1841, after Queen Frederica's death, to leave standing the Altes Palais, where the two had lived since arriving in Hanover. Ernest's interest in and support of the railroads led to Hanover becoming a major railway junction, much to the nation's benefit. However, when court architect Georg Ludwig Friedrich Laves in 1837 proposed the building of an opera house in Hanover, the King initially refused, calling the proposal "this utterly absurd idea of building a court theatre in the middle of this green field". The King finally gave his consent in 1844 and the opera house opened in 1852, a year after the King's death.

Every week, the King travelled with his secretary to different parts of his kingdom, and anyone could lay a petition before him—although Ernest had petitions screened by the secretary so he would not have to deal with frivolous complaints. Ernest opened high ministerial positions to those of any class, securing the services of several ministers who would not have been eligible without this reform. Though the King had, while Duke of Cumberland, fought against Catholic emancipation in Britain and Ireland, he made no objection to Catholics in government service in Hanover and even visited their churches. Ernest explained this by stating that there were no historical reasons to restrict Catholics in Hanover, as there had been in the United Kingdom. He continued to oppose admission of Jews into the British Parliament, but gave Jews in Hanover equal rights.

The King supported a postal union and common currency among the German states, but opposed the Prussian-led customs union, the Zollverein, fearing that it would lead to Prussian dominance and the end of Hanover as an independent state. Instead, the King supported the Steuerverein, which Hanover and other western German states had formed in 1834. When the Steuerverein treaties came up for renewal in 1841, Brunswick pulled out of the union and joined the Zollverein, greatly weakening Hanover's position, especially since Brunswick had enclaves within Hanover. Ernest was able to postpone the enclaves' entry into the Zollverein and, when a trade war began, was able to outlast Brunswick. In 1845, Brunswick, Hanover and Prussia signed a trade agreement. In 1850, Ernest reluctantly permitted Hanover to join the Zollverein, though the entry was on favourable terms. Ernest's forebodings about Prussia were warranted; in 1866, fifteen years after his death, Hanover chose the Austrian side in the Austro-Prussian War, was defeated and was annexed by Prussia.

Hanover was little affected by the revolutions of 1848; a few small disturbances were put down by the cavalry without bloodshed. When agitators arrived from Berlin at the end of May 1848 and there were demonstrations outside the King's palace, Ernest sent out the Prime Minister. The Prime Minister warned that, if the demonstrators made any inappropriate demands on the King, Ernest would pack up his things and leave for Britain, taking the Crown Prince with him. This would leave the country at the mercy of expansionist Prussia and the threat put an end to the agitation. Afterwards, the King granted a new constitution, somewhat more liberal than the 1819 document.

Relations with Britain
Ernest Augustus is supposed to have asked the advice of the Duke of Wellington as to what course he should take after Victoria's accession, with Wellington supposedly saying "Go before you are pelted out." However, Bird dismisses this story as unlikely, given Wellington's customary respect to royalty and the fact that Ernest had little choice in what to do—he had to go to his kingdom as quickly as possible. One decision the new king did have to make was whether, in his capacity as Duke of Cumberland, to swear allegiance to Victoria in the House of Lords. Shortly after William's death, Ernest heard from Lord Lyndhurst that Lord Cottenham, the Lord Chancellor, had stated that he would refuse to administer the Oath of Allegiance to the King, as a foreign sovereign. The King hurriedly appeared in the House of Lords, before his departure for Hanover, and subscribed to the Oath before the Chief Clerk as a matter of routine. Ernest was heir presumptive to Queen Victoria until the birth of her daughter Victoria, Princess Royal, in November 1840. The Lord Privy Seal, Lord Clarendon, wrote, "What the country cares about is to have a life more, whether male or female, between the succession and the King of Hanover."

Almost immediately upon going to Hanover, the King became involved in a dispute with his niece. Queen Victoria had a strained relationship with her mother Victoria, Duchess of Kent, and wanted to give the Duchess accommodation near her, for the sake of appearances—but not too near her. To that end, she asked the King to give up his apartments at St James's Palace in favour of the Duchess. The King, wishing to retain apartments in London in anticipation of frequent visits to England and reluctant to give way in favour of a woman who had frequently fought with his brother, King William, declined and the Queen angrily rented a house for her mother. At a time when the Queen was trying to pay off her father's debts, she saw this as an unnecessary expense. Her ill-feeling towards the King increased when he refused, and advised his two surviving brothers to refuse as well, to give precedence to her intended husband, Prince Albert of Saxe-Coburg and Gotha. Ernest argued that the standing of the various royal families had been settled at the Congress of Vienna and that the King of Hanover should not have to yield to one whom he described as a "paper Royal Highness". The act which naturalised Albert as a British subject left the question of his precedence unresolved.

Matters came to a head when Ernest returned for what would prove to be his only visit to England as King of Hanover, in 1843. He was welcomed warmly, everywhere but at the Palace. At the wedding of Princess Augusta of Cambridge, he attempted to insist on a superior place to that of Prince Albert. The prince, 48 years Ernest's junior, settled things with what Albert described as a "strong push" and carefully wrote his name on the certificate under the Queen's, so close to his wife's as to leave no space for the King's signature. The King apparently held no grudge, as he invited the prince for a stroll in the park. When Albert demurred on the grounds that they might be jostled by crowds, the King replied, "When I lived here I was quite as unpopular as you are and they never bothered me." Shortly after the wedding, the King injured himself in a fall, with Albert writing to his brother, "Happily he fell over some stones in Kew and damaged some ribs." This injury spared him further contact with Victoria and Albert. During his visit, the King found time to take his place as Duke of Cumberland in the House of Lords. Victoria recorded in her journal that the King had stated when asked if he would speak in the Lords, "No, I shall not, unless the Devil prompts me!" The Queen also recorded that though the King greatly enjoyed listening to the debates, he did not himself speak. The King made a point of welcoming British visitors to Hanover and when one Englishwoman told him that she had been lost in the city, the King denied that this was possible, as "the whole country is no larger than a fourpenny bit."

The monarchs engaged in one more battle—over jewels left by Queen Charlotte. Queen Victoria, who possessed them, took the position that they belonged to the British Crown. King Ernest maintained that they were to go to the heir male, that is, himself. The matter was arbitrated, and just as the arbitrators were about to announce a decision in Hanover's favour, one of the arbitrators died, voiding the decision. Despite the King's request for a new panel, Victoria refused to permit one during the King's lifetime and took every opportunity to wear the jewels, causing the King to write to his friend, Lord Strangford, "The little Queen looked very fine, I hear, loaded down with my diamonds." The King's son and successor, King George V, pressed the matter, and in 1858, after another decision in Hanover's favour, the jewels were turned over to the Hanoverian ambassador.

Later life, death, and memorial
In 1851, the King undertook a number of journeys around Germany. He accepted an invitation from the Queen of Prussia to visit Charlottenburg Palace, near Berlin. He visited Mecklenburg for the christening of the Grand Duke's son and Lüneburg to inspect his old regiment. In June, Ernest celebrated his 80th birthday by playing host to the King of Prussia. Late that summer, he visited Göttingen, where he opened a new hospital and was given a torchlight procession.

The King continued his interest in British affairs and wrote to Lord Strangford about the Great Exhibition of 1851: The folly and absurdity of the Queen in allowing this trumpery must strike every sensible and well-thinking mind, and I am astonished the ministers themselves do not insist on her at least going to Osborne during the Exhibition, as no human being can possibly answer for what may occur on the occasion. The idea ... must shock every honest and well-meaning Englishman. But it seems everything is conspiring to lower us in the eyes of Europe.

The King died on 18 November 1851 after an illness of about a month. He was mourned greatly in Hanover; less so in the United Kingdom, where The Times omitted the customary black border to its front page and claimed "the good that can be said of the Royal dead is little or none." Both he and Queen Frederica rest in a mausoleum in the Berggarten of Herrenhausen Gardens.

A large equestrian statue of King Ernest Augustus may be found in a square named after him in front of Hanover Central Station, inscribed with his name and the words (in German) "To the father of the nation from his loyal people." It is a popular meeting place; in the local phrase, people arrange to meet unterm Schwanz or "under the tail".

Although The Times denigrated Ernest's career as Duke of Cumberland, it did speak well of his time as King of Hanover and of his success in keeping Hanover stable in 1848:

Above all, he possessed a resolute decision of character, which, however unfortunately it may have operated under different conditions, appeared to extraordinary advantage at the crisis of continental thrones. Bewildered by the revolutionary din, and oscillating ignominiously between fear and rage, resistance and concession, the clique of crowned heads suffered greatly by contrast with a Sovereign who at least knew his own mind and was prepared to abide by his opinions. In the European convulsions, therefore, King Ernest maintained the stability of his throne and the tranquillity of his people without damage from revolution or reaction. As Kings, indeed, are computed on the continent, he was an able and even a popular Monarch, and his memory may find, perhaps, in his ancestral dominions a sympathy which it would be vain to bespeak for it in the scenes of his manhood or the land of his birth.

Titles and styles

 * 5 June 1771 – 23 April 1799: His Royal Highness Prince Ernest Augustus
 * 23 April 1799 – 20 June 1837: His Royal Highness The Duke of Cumberland and Teviotdale
 * 20 June 1837 – 18 November 1851: His Majesty The King of Hanover

British and Hanoverian

 * Knight of the Garter (KG) – nominated 2 June 1786
 * Privy Council of Great Britain (later of the United Kingdom) (PC) – 5 June 1799. (He was senior PC of the United Kingdom from 1847 until his death.)
 * Knight of the Order of the Thistle (KT)
 * Knight Grand Cross of the Order of the Bath (GCB) – 2 January 1815
 * Knight Grand Cross of the Royal Guelphic Order (GCH in British usage) (Kingdom of Hanover) – 12 August 1815; became sovereign of the order on succeeding to the Hanoverian throne 20 June 1837.
 * Knight of St Patrick (KP) – 20 August 1821
 * Order of St George (Kingdom of Hanover) - founder and sovereign of the order, 23 April 1839.
 * Fellow of the Royal Society (FRS) – 24 April 1828

Foreign

 * Grand Cross of Albert the Bear – 13 January 1839 (Ascanian duchies)
 * Grand Cross of the Order of St. Stephen – 1839 (Austria)
 * Grand Cross of the House Order of Fidelity – 1829 (Baden)
 * Knight of the Elephant – 7 July 1838 (Denmark)
 * Grand Cross of the Saxe-Ernestine House Order – August 1839 (Ernestine duchies)
 * Knight of the Black Eagle – 21 May 1815 (Prussia)
 * Grand Cross of the Red Eagle (Prussia)
 * Grand Cross of the Ludwig Order (Hesse and by Rhine)
 * Grand Cross of the Golden Lion – 20 September 1818 (Hesse-Kassel)
 * Knight of St. Hubert – 1826 (Bavaria)
 * Grand Cross of the Military William Order – 3 July 1849 (Netherlands)
 * Knight of St. Andrew – September 1819 (Russia)

title: Ernest Augustus, King of Hanover