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Chapter 36: Q66P (page 1113)
An x-ray beam of a certain wavelength is incident on an NaCl crystal, at to a certain family of reflecting planes of spacing. If the reflection from those planes is of the first order, what is the wavelength of the x rays?
The wavelength of the x rays will be .
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In a double-slit experiment, the slit separation d is 2.00 times the slit width w. How many bright interference fringes are in the central diffraction envelope?
Figure 36鈥�35 shows the bright fringes that lie within the central diffraction envelope in two double-slit diffraction experiments using the same wavelength of light. Is (a) the slit width , (b) the slit separation , and (c) the ratio in experiment B greater than, less than, or the same as those quantities in experiment A?
Floaters. The floaters you see when viewing a bright, featureless background are diffraction patterns of defects in the vitreous humor that fills most of your eye. Sighting through a pinhole sharpens the diffraction pattern. If you also view a small circular dot, you can approximate the defect鈥檚 size. Assume that the defect diffracts light as a circular aperture does. Adjust the dot鈥檚 distance L from your eye (or eye lens) until the dot and the circle of the first minimum in the diffraction pattern appear to have the same size in your view. That is, until they have the same diameter on the retina at distance from the front of the eye, as suggested in Fig. 36-42a, where the angles on the two sides of the eye lens are equal. Assume that the wavelength of visible light is . If the dot has diameter and is distance from the eye and the defect is in front of the retina (Fig. 36-42b), what is the diameter of the defect?
A diffraction grating has resolving power . (a) Show that the corresponding frequency range f that can just be resolved is given by . (b) From Fig. 36-22, show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by . (c) Show that , this relation being independent of the various grating parameters. Assume .
Figure 36-46 is a graph of intensity versus angular positionfor the diffraction of an x-ray beam by a crystal. The horizontal scale is set by.The beam consists of two wavelengths, and the spacing between the reflecting planes is. What are the (a) shorter and (b) longer wavelengths in the beam?
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