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White light illuminates two slits separated by distance b in a Young's double slit experiment. The screen is at distance d (>>b) from the slits. At a point on the screen directly in front of one of the slits, which of the following wavelengths are missing? (1) lambda = b²/d (2) lambda = 2*b²/d (3) lambda = b²/(3d) (4) lambda = 2*b²/(3d). Choose the correct option.

1. 1 and 3
2. 1 and 2
3. 2 and 4
4. 3 and 4

Correct answer: 1 and 3

Solution

The point P is directly in front of one slit, at a lateral distance of b/2 from the midpoint (central axis). Path difference at P: delta = b*(b/2)/d = b²/(2d). A wavelength is missing (dark fringe / destructive interference) when delta = (2n+1)*lambda/2 for integer n >= 0. So lambda = 2*delta/(2n+1) = b²/((2n+1)*d). For n=0: lambda = b²/d (option 1). For n=1: lambda = b²/(3d) (option 3). Options 2 and 4 correspond to bright fringe conditions. Missing wavelengths: 1 and 3.

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