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Figure 19-12 A transmission grating spectrum is created by jewelry made with replica gratings (a) Compact discs act as reflection gratings, creating a spectrum diffraction pattern when they are placed under white light (b)

Measuring wavelength An instrument used to measure light wavelengths using a diffraction grating is called a grating spectroscope, as shown in the diagram in Figure 19-13 The source to be analyzed emits light that is directed to a slit The light from the slit passes through a diffraction grating The grating produces a diffraction pattern that is viewed through a telescope The diffraction pattern produced by a diffraction grating has narrow, equally spaced, bright lines, as shown in Figure 19-14 The larger the number of slits per unit length of the grating, the narrower the lines in the diffraction pattern As a result, the distance between the bright lines can be measured much more precisely with a grating spectroscope than with a double slit Earlier in this chapter, you found that the interference pattern produced by a double slit could be used to calculate wavelength An equation for the diffraction grating can be developed in the same way as for the double slit However, with a diffraction grating, could be large, so the small angle simplification does not apply Wavelength can be found by measuring the angle, , between the central bright line and the first-order bright line Wavelength from a Diffraction Grating d sin

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The wavelength of light is equal to the slit separation distance times the sine of the angle at which the first-order bright line occurs

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Constructive interference from a diffraction grating occurs at angles on either side of the central bright line given by the equation m dsin , where m 0, 1, 2, etc The central bright line occurs at m 0

Figure 19-14 A grating was used to produce diffraction patterns for red light (a) and white light (b)

n C#, you can give local variables only those names that allow them to be uniquely identified in a given scope. If a name has more than one meaning in a scope and you have no way to disambiguate the name, the innermost declaration of the name is an error and you must change it. Consider the following: using System; class MyObject { public MyObject(int x, int y) { this.x = x; this.y = y; } int x; int y; } In the constructor, x refers to the parameter named x because parameters take precedence over member variables. To access the instance variable named x, it must be prefixed with this., which indicates it must be an instance variable. The preceding construct is preferred over renaming the constructor parameters or member variables to avoid the name conflict.1 In the following situation, you have no way to name both variables, and the inner declaration is therefore an error: // error using System; class MyObject {

Using a DVD as a Diffraction Grating A student noticed the beautiful spectrum reflected off a rented DVD She directed a beam from her teacher s green laser pointer at the DVD and found three bright spots reflected on the wall The label on the pointer indicated that the wavelength was 532 nm The student found that the spacing between the spots was 129 m on the wall, which was 125 m away What is the spacing between the rows on the DVD

Sketch the experiment, showing the DVD as a grating and the spots on the wall Identify and label the knowns Known:

Unknown:

125 m

459

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