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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

The continue statement skips all the later lines in the current iteration statement and then continues executing the iteration statement.

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

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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

Figure 19-8 Notice the wide central band and the narrower bands on either side A single-slit diffraction pattern for red light would have a wider central band than blue light as long as the same size slit is used for both colors

Figure 19-9 A slit of width w is divided into pairs of lines that form Huygens wavelets, each pair separated by w/2

The goto statement can jump directly to a label. Because using goto statements is widely considered to be harmful,5 C# prohibits some of their worst abuses. A goto can t be used to jump into a statement block, for example. The only place where their use is recommended is in switch statements or to transfer control to outside a nested loop (though they can be used elsewhere).

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w 2 2

Figure 19-10 This diagram represents an analysis of the first dark band The distance to the screen, L, is much larger than the slit width, w (Illustration not to scale)

P0 (central bright band)

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