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Chapter 36: Q69P (page 1113)
X rays of wavelength are found to undergo second order reflection at a Bragg angle offrom a lithium fluoride crystal. What is the interplanar spacing of the reflecting planes in the crystal?
The inter planar spacing of the reflecting planes in the crystal is .
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(a) How many bright fringes appear between the first diffraction-envelope minima to either side of the central maximum in a double-slit pattern if , , and ? (b) What is the ratio of the intensity of the third bright fringe to the intensity of the central fringe?
Manufacturers of wire (and other objects of small dimension) sometimes use a laser to continually monitor the thickness of the product. The wire intercepts the laser beam, producing a diffraction pattern like that of a single slit of the same width as the wire diameter (Fig.). Suppose a helium 鈥� neon laser, of wavelength , illuminates a wire, and the diffraction pattern appears on a screen at distance . If the desired wire diameter is , what is the observed distance between the two tenth-order minima (one on each side of the central maximum)?
Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booster rockets at ranges up to 2000 km. One limitation on such a device is the spreading of the beam due to diffraction, with resulting dilution of beam intensity. Consider such a laser operating at a wavelength of 1.40 nm. The element that emits light is the end of a wire with diameter 0.200 mm. (a) Calculate the diameter of the central beam at a target 2000 km away from the beam source. (b) What is the ratio of the beam intensity at the target to that at the end of the wire? (The laser is fired from space, so neglect any atmospheric absorption.)
At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer鈥檚 eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?
Light of wavelength 600 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by and .The fourth order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width , what are the (c) largest, (d) second largest, and (e) third largest values of the order of the maxima produced by the grating?
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