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In a Young's double-slit experiment, one slit is covered with glass of refractive index mu1 = 1.4 and the other with glass of refractive index mu2 = 1.7, both of the same thickness t. The central maximum of the original pattern is now occupied by the third bright fringe. If the wavelength of light used is 4000 Angstrom, find the thickness t in micrometers.

1. 1.0
2. 2.0
3. 3.0
4. 4.0

Correct answer: 4.0

Solution

Each slab introduces extra path (mu - 1)*t compared to air. Net path difference = (mu2 - 1)*t - (mu1 - 1)*t = (mu2 - mu1)*t = (1.7 - 1.4)*t = 0.3t. For the central maximum to shift to the third bright fringe: 0.3t = 3 * lambda = 3 * 4000 Angstrom = 12000 Angstrom = 1.2 micrometers. t = 1.2/0.3 = 4 micrometers.

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