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 the of a relaxed eye with the pupil fully dilated to localid="1648735653936" ? model the eye as a single lens localid="1648735646217" in front of the retina.
A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle u2. Wavelengths for which the index of refraction is n + dn, where dn V n, are refracted at angle u2 + du.
a. Show that the angular separation of the two wavelengths, in radians, is du = -1dn/n2 tan u2.
b. A beam of white light is incident on a piece of glass at 30.0°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?
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’s 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?
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 microscope has a tube length. What focal-length objective will give total magnification localid="1649845070556" when used with an eyepiece having a focal length ?
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