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Light of wavelength 560 nm passes through a circular pinhole of diameter 0.20 mm and falls on a wall 2.00 m away. Estimate the radius of the central bright spot (central diffraction maximum) formed on the wall.

1. About 3.4 mm
2. About 6.8 mm
3. About 1.7 mm
4. About 11 mm

Correct answer: About 6.8 mm

Solution

For a circular aperture the first dark ring is at angular radius theta = 1.22*lambda/D. Here lambda = 560 nm = 5.6e-7 m, D = 0.20 mm = 2.0e-4 m, L = 2.00 m. theta = 1.22 * 5.6e-7 / 2.0e-4 = 1.22 * 2.8e-3 = 3.416e-3 rad. Radius r = theta*L = 3.416e-3 * 2.00 = 6.83e-3 m approx 6.8 mm.

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