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In Young’s double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths λ₁ = 12000 Å and λ₂ = 10000 Å. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

1. 6 mm
2. 3 mm
3. 8 mm
4. 4 mm

Correct answer: 3 mm

Solution

The condition for coinciding bright fringes is that the path difference for both wavelengths must be an integer multiple of their respective wavelengths. Using the formula for fringe position, y = (nλD)/d, and solving for the least common multiple (LCM) of λ₁ and λ₂, we find the minimum distance to be 3 mm.

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