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In a double-slit experiment with monochromatic light, fringes form on a screen at some distance from the slits. When the screen is moved 5e-2 m closer to the slits, the fringe width changes by 3e-3 cm. If the slit separation is 1 mm, what is the wavelength of the light (in nm)?

1. 600 nm
2. 500 nm
3. 650 nm
4. 450 nm

Correct answer: 600 nm

Solution

Fringe width beta = lambda*D/d, so delta(beta) = lambda*delta(D)/d. Given delta(beta) = 3e-3 cm = 3e-5 m, delta(D) = 5e-2 m, d = 1 mm = 1e-3 m. Then lambda = d*delta(beta)/delta(D) = (1e-3 * 3e-5)/(5e-2) = 3e-8/5e-2 = 6e-7 m = 600 nm.

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