Telescopes and cameras
"In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view; conversely, shorter focal length or higher optical power is associated with a wider angle of view."^{[1]}
ContentsEvaluation

Problem 1[edit]
"For the case of a [doubleconvex] lens of thickness d in air, and surfaces with radii of curvature R_{1} and R_{2}, the effective focal length f is given by:
 '"`UNIQpostMath00000003QINU`"'
where n is the refractive index of the lens medium. The quantity 1/f is also known as the optical power of the lens."^{[1]}
What is the formula for a planoconvex lens?
Calculate the focal length of a double convex lens in which R_{1} = 10 m and R_{2} = 200 m. Let n = 1.732 and d = 2 cm.
What is the focal length of a hemispherical planoconvex lens of radius 10 m? Let n= 1.324 and d = 1 dm.
What is a likely focal length for a planoconvex lens where the convex surface is parabolic rather than spherical?
Problem 2[edit]
For a focal length of 100 mm, what are the aperture or entrance pupil diameters for each of the apertures shown if no optical components are between the entrance pupil and the aperture?
For a simple camera or telescope with an aperture lens diameter of 5 m, what is the focal length for each of the apertures or entrance pupil diameters in the diagram if no optical components are between the entrance pupil and the aperture?
For the following pairs of focal lengths and lens diameters, what would be the fnumbers? (a) 5 m, 3 m (b) 10 m, 3 mm (c) 50 cm, 2 m (d) 15 km, 25 m (e) 5,000 km, 16 cm.
Problem 3[edit]
The lens in the image at right has an aperture range of '"`UNIQpostMath00000005QINU`"' to '"`UNIQpostMath00000006QINU`"'
The image lens at right uses "a standard fstop scale, which is an approximately geometric sequence of numbers that corresponds to the sequence of the powers of the square root of 2: '"`UNIQpostMath00000007QINU`"' '"`UNIQpostMath00000008QINU`"' '"`UNIQpostMath00000009QINU`"' '"`UNIQpostMath0000000AQINU`"' '"`UNIQpostMath0000000BQINU`"' '"`UNIQpostMath0000000CQINU`"' '"`UNIQpostMath0000000DQINU`"' '"`UNIQpostMath0000000EQINU`"' '"`UNIQpostMath0000000FQINU`"' [and] '"`UNIQpostMath00000010QINU`"'"^{[2]}
"The sequence above is obtained by approximating the following exact geometric sequence:"^{[2]}
 '"`UNIQpostMath00000011QINU`"'
 '"`UNIQpostMath00000012QINU`"'
 '"`UNIQpostMath00000013QINU`"'
 '"`UNIQpostMath00000014QINU`"'
 '"`UNIQpostMath00000015QINU`"'
 '"`UNIQpostMath00000016QINU`"'
 '"`UNIQpostMath00000017QINU`"'
 '"`UNIQpostMath00000018QINU`"'
 '"`UNIQpostMath00000019QINU`"'
 '"`UNIQpostMath0000001AQINU`"'
What are the missing terms?
"Each "stop" is marked with its corresponding fnumber, and represents a halving of the light intensity from the previous stop. This corresponds to a decrease of the pupil and aperture diameters by a factor of 1/'"`UNIQpostMath0000001BQINU`"' or about 0.7071, and hence a halving of the area of the pupil."^{[2]}
For a lens diameter of 35 mm, what is the focal length for each fstop?
Problem 4[edit]
"[S]hutter speeds are arranged so that each setting differs in duration by a factor of approximately two from its neighbour. Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time. Therefore to have the same exposure at this larger aperture as at the previous aperture, the shutter would be opened for half as long (i.e., twice the speed). The film will respond equally to these equal amounts of light, since it has the property of reciprocity. This is less true for extremely long or short exposures, where we have reciprocity failure. Aperture, shutter speed, and film sensitivity are linked: for constant scene brightness, doubling the aperture area (one stop), halving the shutter speed (doubling the time open), or using a film twice as sensitive, has the same effect on the exposed image."^{[2]}
"[S]hutter speed or exposure time is the length of time a camera's shutter is open when taking a photograph.^{[3]} The amount of light that reaches the film or image sensor is proportional to the exposure time."^{[4]}
"Exposure value (EV) is a single quantity that accounts for the shutter speed and the fnumber."^{[4]}
"Multiple combinations of shutter speed and fnumber can give the same exposure value."^{[4]}
"Doubling the exposure time doubles the amount of light (subtracts 1 EV). Making the fnumber one stop brighter (reducing the fnumber by a factor of '"`UNIQpostMath0000001CQINU`"') also doubles the amount of light. A shutter speed of 1/50 s with an '"`UNIQpostMath0000001DQINU`"' lens gives the same exposure value as a 1/100 s shutter with an {'"`UNIQpostMath0000001EQINU`"' lens, and also the same exposure value as a 1/200 s shutter with an '"`UNIQpostMath0000001FQINU`"' lens."^{[4]}
A "standardized 2:1 scale ... for shutter speed [is such] that opening one aperture stop and reducing the shutter speed by one step resulted in the identical exposure. The ... standards for shutter speeds are:^{[5]}"^{[4]}
 1/16000 s
 1/12000 s
 1/8000 s
 1/4000 s
 1/2000 s
 1/1000 s
 1/500 s
 1/250 s
 1/125 s
 1/60 s
 1/30 s
 1/15 s
 1/8 s
 1/4 s
 1/2 s
 1 s
What are the other fnumbers that match the shutter speeds?
"[E]xposure value (EV) is a number that represents a combination of a camera's shutter speed and fnumber, such that all combinations that yield the same exposure have the same EV value (for any fixed scene luminance). Exposure value also is used to indicate an interval on the photographic exposure scale, with 1 EV corresponding to a standard powerof2 exposure step, commonly referred to as a stop."^{[6]}
"Exposure value is a base2 logarithmic scale [...]:
 '"`UNIQpostMath00000020QINU`"'
where
 N is the relative aperture (fnumber)
 t is the exposure time (“shutter speed”) in seconds".^{[6]}
"In a mathematical expression involving physical quantities, it is common practice to require that the argument to a transcendental function (such as the logarithm) be dimensionless. The definition of EV ignores the units in the denominator and uses only the numerical value of the exposure time in seconds; EV is not the expression of a physical law, but simply a number for encoding combinations of camera settings."^{[6]}
Match up the shutter speeds with fnumbers to give the same EV.
Hypotheses[edit]
 Alternate title could be Radiation telescopes/Problem set.
 See also: Control groups, Proof of concept, and Proof of technology
See also[edit]
References[edit]
 ↑ ^{1.0} ^{1.1} Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
 ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
 ↑ Sidney F. Ray (2000). "Camera Features". In Ralph Eric Jacobson et al.. Manual of Photography: A Textbook of Photographic and Digital Imaging (Ninth ed. ed.). Focal Press. pp. 131–2. ISBN 0240515749. http://books.google.com/books?id=HHX4xB94vcMC&pg=PA132&ots=7Gq_Az_zl&sig=bQ5bvKISy1_Q4km6PmyCZDcGo.
 ↑ ^{4.0} ^{4.1} ^{4.2} ^{4.3} ^{4.4} Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
 ↑ Cub Kahn (1999). Essential Skills for Nature Photography. Amherst Media. ISBN 1584280093. http://books.google.com/books?id=EZhNYTZjIC&pg=PT21&ei=h0MHSejTFI_gswOh3eDzDQ.
 ↑ ^{6.0} ^{6.1} ^{6.2} Lua error in Module:Citation/CS1 at line 3505: bad argument #1 to 'pairs' (table expected, got nil).
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