X

sin 0min = — (Angle of destructive interference; (5.6)

slit interference)

In contrast, the rays directed straight ahead at 0 = 0 (Fig. 6a) are all in constructive interference.

A proper summation of the phases and amplitudes of all the wavelets over the narrow slit for each angle 0 leads to an intensity pattern of the form, sin2 B ( ud \

slit diffraction)

This function (Fig. 6c) has a maximum value of 1.0 at B = 0, or 0 = 0. It has minima with zero value when sin B = 0, i.e., at B = ±nu, where n is an integer > 1. The first minimum at B = ' corresponds to the angle sin 0min — X/d shown in Fig. 6b. The second minimum is at B = 2u, or sin 0min = 2X/d. Thus the minima will generally be separated by A0 ~ X/d for small angles, 0 ^ 1 so that sin 0 ~ 0. The two central minima are an exception; they are separated by twice this amount.

The circular aperture of a telescope mirror yields a circular diffraction pattern as expected from the symmetry. Again, a proper summation of the wavelets must be carried out to obtain the radial variation of brightness. The result is similar in form to Fig. 6c. It turns out that the angular radius 0min of the first minimum (dark ring), which encircles most of the light, for X ^ d, is

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