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White light passes through a double slit and interference is observed on a screen 1.5 m away. The slit separation is 0.3 mm. The first violet and first red fringes appear 2.0 mm and 3.5 mm from the central white fringe, respectively. The difference between the wavelengths of red and violet light is _____ nm.

1. 300 nm
2. 150 nm
3. 450 nm
4. 200 nm

Correct answer: 300 nm

Solution

For the first-order bright fringe, y = lambda*D/d, so lambda = y*d/D. Violet: lambda_v = (2.0e-3)(0.3e-3)/1.5 = 4.0e-7 m = 400 nm. Red: lambda_r = (3.5e-3)(0.3e-3)/1.5 = 7.0e-7 m = 700 nm. Difference = 700 - 400 = 300 nm.

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