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Red light of wavelength 6500 angstrom from a distant source is incident on a single slit 0.50 mm wide. On a screen 1.8 m from the slit, find the distance between the first dark fringes on the two sides of the central maximum.

1. 4.7 mm
2. 2.3 mm
3. 9.4 mm
4. 1.2 mm

Correct answer: 4.7 mm

Solution

The first dark fringe lies at y1 = lambda*D/a. The two first dark fringes (one on each side) are separated by 2*y1 = 2*lambda*D/a = 2*(6500e-10)*(1.8)/(0.5e-3) = 2*(6.5e-7*1.8/5e-4) = 2*(1.17e-6/5e-4) = 2*2.34e-3 = 4.68e-3 m = 4.7 mm.

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