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Chapter 35: Q. 18 (page 1017)
A telescope has a diameter objective lens. What minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source?
The minimum diameter is.
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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′ = 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
“stop down” to smaller apertures
A narrow beam of white light is incident on a sheet of quartz. The beam disperses in the quartz, with red light traveling at an angle of with respect to the normal and violet light traveling at . The index of refraction of quartz for red light is . What is the index of refraction of quartz for violet light?
A tall man is in front of a camera with a focal length lens. How tall is his image on the detector?
The center of the galaxy is filled with low-density hydrogen gas that scatters light rays. An astronomer wants to take a picture of the center of the galaxy. Will the view be better using ultraviolet light, visible light, or infrared light? Explain.
A sheet of glass has and . A narrow beam of white light is incident on the glass at . What is the angular spread of the light inside the glass?
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