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Chapter 35: Q. 8 (page 1017)
What is the aperture diameter of a focal-length lens set to
The Diameter of the aperture is.
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What is theof a lens with a focal length and adiameter aperture?
The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650 nm.
a. What鈥檚 the distance (in km) between two stars that are marginally resolved? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.
b. For comparison, what is this distance as a multiple of the distance of Jupiter from the sun?
A -tall object is from a screen. A diverging lens with focal lengthis in front of the object. What are the focal length and distance from the screen of a second lens that will produce a well-focused, -tall image on the screen?
A hydrogen discharge lamp emits light with two prominent wavelengths: (red) and (blue). The light enters
a flint-glass prism perpendicular to one face and then refracts
through the hypotenuse back into the air. The angle between
these two faces is .
a. Use Figure to estimate to the index of refraction
of flint glass at these two wavelengths.
b. What is the angle (in degrees) between the red and blue light
as it leaves the prism?
The resolution of a digital camera is limited by two factors:
diffraction by the lens, a limit of any optical system, and the fact
that the sensor is divided into discrete pixels. Consider a typical
point-and-shoot camera that has a 20-mm-focal-length lens and
a sensor with 2.5@mm@wide pixels.
a. First,ass ume an ideal, diffractionless lens. At a distance of
100 m, what is the smallest distance, in cm, between two
point sources of light that the camera can barely resolve? In
answering this question, consider what has to happen on the
sensor to show two image points rather than one. You can use
s鈥� = f because s W f.
b. You can achieve the pixel-limited resolution of part a only if
the diffraction width of each image point is no greater than
1 pixel in diameter. For what lens diameter is the minimum
spot size equal to the width of a pixel? Use 600 nm for the
wavelength of light.
c. What is the f-number of the lens for the diameter you found in
part b? Your answer is a quite realistic value of the f-number
at which a camera transitions from being pixel limited to
being diffraction limited. For f-numbers smaller than this
(larger-diameter apertures), the resolution is limited by the
pixel size and does not change as you change the aperture. For
f-numbers larger than this (smaller-diameter apertures), the
resolution is limited by diffraction, and it gets worse as you
鈥渟top down鈥� to smaller apertures
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