Chapter 35: Q. 8 (page 1016)
To focus parallel light rays to the smallest possible spot, should you use a lens with a small f-number or a large f-number? Explain.
smaller f-numbered lens
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What is the f-number of a relaxed eye with the pupil fully dilated to mm? model the eye as a single lens 2.4 cm in front of the retina
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 common optical instrument in a laser laboratory is a beam expander. one type of beam expander is shown in FIGURE P.
a. For what lens spacing d does a parallel laser beam exit from
the right?
b. What is the width of the exiting laser beam?
Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you’re farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power and your right eye’s lens is . a. Which lens should you use for the objective and which for the eyepiece? Explain.
b. What will be the magnification of your telescope?
c. How far apart should the two lenses be when you focus on distant objects?
A microscope with a tube length of achieves a total magnification of with a objectives and a eye piece. The microscope is focused for viewing with a related eye. how far is the sample from the objective lens?
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