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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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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
An astronomer is trying to observe two distant stars. The stars are marginally resolved when she looks at them through a filter that passes green light with a wavelength near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere.
A. Changing the filter to a different wavelength. If so, should she use a shorter or a longer wavelength?
B. Using a telescope with an objective lens of the same diameter but a different focal length. If so, should she select a shorter or a longer focal length?
C. Using a telescope with an objective lens of the same focal length but a different diameter. If so, should she select a larger or a smaller diameter?
D. Using an eyepiece with a different magnification. If so, should she select an eyepiece with more or less magnification?
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?
A -tall object is to the left of a lens with a focal length of . A second lens with a focal length of is to the right of the first lens.
a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.
b. Calculate the image position and height. Compare with your ray-tracing answers in part a.
High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun light to a small spot that can burn things. As an engineer you have designed a laser cutting device in which the material to be cut is placed behind the lens. you have selected a high-power laser with a wavelength of
your calculation indicates that the laser must be focused to a spot in order to have sufficient power to make the cut. what is the minimum diameter of lens you must install?
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