The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See Fig. 36-8b.) (a) Show that the intensity drops to one-half the maximum value when sin2 a ! a2 /2. (b) Verify that a ! 1.39 rad (about 80) is a solution to the transcendental equation of (a). (c) Show that the FWHM is 2u ! 2 sin&1 (0.443l/a), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00l,(e) 5.00l,and (f) 10.0l

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