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Chapter 35: Q.1. (page 1016)
Suppose you wanted special glasses designed to let you see underwater without a face mask. Should the glasses use a converging or diverging lens? Explain.
Glasses with converging lenses
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White light is incident onto a prism at the angle shown in . violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is larger than the index of refraction of red light. At what angle does red light emerges from the rear face?
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鈥� = 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
鈥渟top down鈥� to smaller apertures
White light is incident onto a prism at the shown in Figure . Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is larger than the index of refraction of red light. At what does red light emerges from the rear face?
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?
Modern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in Figure 35.14 with a photo-ocular that focuses the image of the objective to a real image on the sensor of a digital camera. A typical sensor is 22.5 mm wide and consists of 5625 4.0@mm@ wide pixels. Suppose a microscopist pairs a 40* objective with a 2.5* photo-ocular.
a. What is the field of view? That is, what width on the microscope stage, in mm, fills the sensor?
b. The photo of a cell is 120 pixels in diameter. What is the cell鈥檚 actual diameter, in mm?
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