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You have several unknown substances and wish to use a single-slit diffraction apparatus to determine what each one is You decide to place a sample of an unknown substance in the region between the slit and the screen and use the data that you obtain to determine the identity of each substance by calculating its index of refraction 1 Come up with a general formula for the index of refraction

of an unknown substance in terms of the wavelength of the light, vacuum, the width of the slit, w, the distance from the slit to the screen, L, and the distance between the central bright band and the first dark band, x1

The checked and unchecked statements control whether exceptions are thrown if conversions or expressions overflow; see 14.

2 If the source you used had a wavelength of 634 nm,

the slit width was 010 mm, the distance from the slit to the screen was 115 m, and you immersed the apparatus in water (nsubstance 133), then what would you expect the width of the center band to be

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ADCval) Since ADCval is a word variable, its largest possible value is 65,535 so it can have as many as five digits Therefore, we need to include five variables to hold each possible digit of ADCval I could have declared the five variables as tenthousands, thousands, hundreds, tens, and units, but this is one of the few times that I think it s better to directly use the default variable names instead By using the variable names b4 through b0, each name tells us which digit it is (just think in terms of powers of 10); 104 the ten-thousands digit, 103 the thousands digit, etc Of course, if you use this approach, it s important to not declare variables b4 through b0 for another use in the same program

.

Although double-slit interference and single-slit diffraction depend on the wavelength of light, diffraction gratings, such as those shown in Figure 19-11, are used to make precision measurements of wavelength A diffraction grating is a device made up of many single slits that diffract light and form a diffraction pattern that is an overlap of singleslit diffraction patterns Diffraction gratings can have as many as 10,000 slits per centimeter That is, the spacing between the slits can be as small as 10 6 m, or 1000 nm One type of diffraction grating is called a transmission grating A transmission grating can be made by scratching very fine lines with a diamond point on glass that transmits light The spaces between the scratched lines act like slits A less expensive type of grating is a replica grating A replica grating is made by pressing a thin plastic sheet onto a glass grating When the plastic is pulled away, it contains an accurate imprint of the scratches Jewelry made from replica gratings, shown in Figure 19-12a, produces a spectrum Reflection gratings are made by inscribing fine lines on metallic or reflective glass surfaces The color spectra produced when white light reflects off the surface of a CD or DVD is the result of a reflection grating, as shown in Figure 19-12b If you were to shine monochromatic light on a DVD, the reflected light would produce a diffraction pattern on a screen Transmission and reflection gratings produce similar diffraction patterns, which can be analyzed in the same manner Holographic diffraction gratings produce the brightest spectra They are made by using a laser and mirrors to create an interference pattern consisting of parallel bright and dark lines The pattern is projected on a piece of metal that is coated with a light-sensitive material The light produces a chemical reaction that hardens the material The metal is then placed in acid, which attacks the metal wherever it was not protected by the hardened material The result is a series of hills and valleys in the metal identical to the original interference pattern The metal can be used as a reflection grating or a replica transmission grating can be made from it Because of the sinusoidal shape of the hills and valleys, the diffraction patterns are exceptionally bright.

Figure 19-1 Diffraction 1 gratings are used to create diffraction patterns for the analysis of light sources

5. See Go To Statement Considered Harmful, by Edsger W. Dijkstra, at http://www.acm.org/classics/ oct95/.

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