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In a Young's double-slit setup the slit separation is 0.5 mm and the screen is 150 cm away. The light contains two wavelengths, 650 nm and 520 nm. Find the smallest distance from the central maximum at which a bright fringe of one wavelength coincides with a bright fringe of the other.

1. 9.75 mm
2. 15.6 mm
3. 1.56 mm
4. 7.8 mm

Correct answer: 7.8 mm

Solution

Bright fringes coincide when n1*lambda1 = n2*lambda2. With lambda1 = 650 nm and lambda2 = 520 nm, the ratio 650/520 = 5/4, so the smallest orders are n1 = 4, n2 = 5. The coincidence position is y = n1*lambda1*D/d = 4 * 650e-9 * 1.5 / 0.5e-3 = 4 * 650e-9 * 3000 = 7.8e-3 m = 7.8 mm.

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