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Chapter 35: Q.14 (page 1017)
A magnifier has a magnification of . How far from the lens should an object be held so that its image is seen at the near-point distance of ? Assume that your is immediately behind the lens.
far from the lens should an object be held so that its image is seen at the near-point distance of .
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FIGURE shows a simple zoom lens in which the magnitudes of both focal lengths are . If the spacing , the image of the converging lens falls on the right side of the diverging lens. Our procedure of letting the image of the first lens act as the object of the second lens will continue to work in this case if we use a negative object distance for the second lens. This is called a virtual object. Consider an object very far to the left of the converging lens. Define the effective focal length as the distance from the midpoint between the lenses to the final image.
a. Show that the effective focal length is
b. What is the zoom for a lens that can be adjusted from to ?
A red card is illuminated by red light. What color will the card appear? What if it’s illuminated by blue light?
In FIGURE P, what are the position, height, and orientation of the final image? Give the position as a distance to the right or left of the lens.
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 scientist needs to focus a helium-neon laser beam to a spot behind a lens
(a) what focal-length lens should she use?
(b) what minimum diameter must the lens have?
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