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Unformatted text preview: Q1 A plane monochromatic light wave, wavelength and frequency f , is incident normally on two identical narrow slits, separated by a distance d , as indicated in Figure 1.1. The light wave emerging at each slit is given, at a distance x in a direction at time t , by )] / ( 2 cos[ x ft a y- = where the amplitude a is the same for both waves. (Assume x is much larger than d ). (i) Show that the two waves observed at an angle to a normal to the slits, have a resultant amplitude A which can be obtained by adding two vectors, each having magnitude a , and each with an associated direction determined by the phase of the light wave. Verify geometrically, from the vector diagram, that cos 2 a A = where sin d = (ii) The double slit is replaced by a diffraction grating with N equally spaced slits, adjacent slits being separated by a distance d . Use the vector method of adding amplitudes to show that the vector amplitudes, each of magnitude a , form a part of a regular polygon with vertices on a circle of radius R given by , sin 2 a R = Deduce that the resultant amplitude is sin sin N a 1 Figure 1.1 d and obtain the resultant phase difference relative to that of the light from the slit at the edge of the grating. (iii) Sketch, in the same graph, sin N and (1/sin ) as a function of . On a separate graph show how the intensity of the resultant wave varies as a function of . (iv) Determine the intensities of the principal intensity maxima....
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