19 Interference and Diffraction
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15 Air dair 127 nm dstep 64 nm
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Figure 19-7 The Morpho butterfly has a blue color that shimmers iridescently (a) An electron microscope is used to view a cross section of the wing looking down the length of the ridges (b) The ridges are steplike structures Matched pairs of light rays from a single step and from multiple steps can interfere (c)
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Thin-film interference also occurs naturally on the wings of the Morpho butterfly, shown in Figure 19-7a The shimmering blue of the butterfly is caused by ridges that project up from the ground scales of the wings, as shown in Figure 19-7b Light is reflected from and refracted through a series of steplike structures, as diagrammed in Figure 19-7c, forming a blue interference pattern that appears to shimmer to those who see the butterfly
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191 Section Review
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10 Film Thickness Lucien is blowing bubbles and holds the bubble wand up so that a soap film is suspended vertically in the air What is the second thinnest width of the soap film at which he could expect to see a bright stripe if the light illuminating the film has a wavelength of 575 nm Assume the soap solution has an index of refraction of 133 11 Bright and Dark Patterns Two very narrow slits are cut close to each other in a large piece of cardboard They are illuminated by monochromatic red light A sheet of white paper is placed far from the slits, and a pattern of bright and dark bands is seen on the paper Describe how a wave behaves when it encounters a slit, and explain why some regions are bright while others are dark 12 Interference Patterns Sketch the pattern described in problem 11
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13 Interference Patterns Sketch what happens to the pattern in problem 11 when the red light is replaced by blue light 14 Film Thickness A plastic reflecting film (n 183) is placed on an auto glass window (n 152) a What is the thinnest film that will reflect yellowgreen light b Unfortunately, a film this thin cannot be manufactured What is the next-thinnest film that will produce the same effect 15 Critical Thinking The equation for wavelength from a double-slit experiment uses the simplification that is small so that sin tan Up to what angle is this a good approximation when your data has two significant figures Would the maximum angle for a valid approximation increase or decrease as you increase the precision of your angle measurement
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Section 191 Interference
Explain how diffraction gratings form diffraction patterns Describe how diffraction gratings are used in grating spectrometers Discuss how diffraction limits the ability to distinguish two closely spaced objects with a lens
n 16, you learned that smooth wave fronts of light spread when they are diffracted around an edge Diffraction was explained using Huygens principle that a smooth wave front is made up of many small point-source wavelets The cutting of coherent light on two edges spaced closely together produces a diffraction pattern, which is a pattern on a screen of constructive and destructive interference of Huygens wavelets
When coherent, blue light passes through a single, small opening that is larger than the wavelength of the light, the light is diffracted by both edges, and a series of bright and dark bands appears on a distant screen, as shown in Figure 19-8 Instead of the nearly equally spaced bands produced by two coherent sources in Young s double-slit experiment, this pattern has a wide, bright central band with dimmer, narrower bands on either side When using red light instead of blue, the width of the bright central band increases With white light, the pattern is a mixture of patterns of all the colors of the spectrum To see how Huygens wavelets produce the diffraction pattern, imagine a slit of width w as being divided into an even number of Huygens points, as shown in Figure 19-9 Each Huygens point acts as a point source of Huygens wavelets Divide the slit into two equal parts and choose one source from each part so that the pair is separated by a distance w/2 This pair of sources produces coherent, cylindrical waves that will interfere For any Huygens wavelet produced in the top half, there will be another Huygens wavelet in the bottom half, a distance w/2 away, that it will interfere with destructively to create a dark band on the screen All similar pairings of Huygens wavelets interfere destructively at dark bands Conversely, a bright band on the screen is where pairings of Huygens wavelets interfere constructively In the dim regions between bright and dark bands, partial destructive interference occurs