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Q.

In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengthsλ1=12000 A0and λ2=10000 A0. 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?

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a

4 mm

b

3 mm

c

8 mm

d

6 mm

answer is D.

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Detailed Solution

Let n1 bright fringe of λ1 coincides with n2 bright fringe of λ2 Then n1λ1Dd=n2λ2Ddor n1λ1=n2λ n1n2=λ2λ1=1000012000=56Let x be given distance. ∴ x=n1λ1DdHere, n1=5, D=2m,d=2mm=2×10−3mλ1=12000A0=12000×10−10m=12×10−7m x=5×12×10−7m×2m2×10−3m=6×10−3m=6mm

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