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Question

In a Young's double - slit experience, the slits are 2mm apart and are illuminated with a mixture of two wavelengths λ0=750nm and λ=900nm. The minimum distance from the common central bright fringe on a screen 2 m away from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other, is

A
1.5mm
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B
3 mm
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C
4.5 mm
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D
6 mm
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Solution

The correct option is C 4.5 mm
y0=n[Dλd] and yn=n(Dλd)
Equating yn and yn,we get
nn=λλ=900750=65
Hence, the first position at which overlapping occurs is
y6=y6=6(2)(750×109)2×103=4.5mm

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