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Question

# In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the 9th bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern. The wavelength of the light used is

A
25007A
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B
2500A
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C
5000A
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D
50007A
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Solution

## The correct option is C 5000A∘Given,d=0.5mmD=100cmX9−X′2=7.5mm. . . . . . . .(1)Condition for bright fringe,Xn=nλDdfor 9th bright fringeX9=9λDdCondition for dark fringe,Xn=(2n−1)2dX′2=(2×2−1)λD2d=3λD2dFrom equation (1)9λDd−3λD2d=7.5×10−3m15λD2d=7.5mmλ=2d15D×7.5mmλ=2×0.5mm15×100cm×7.5mmλ=5000×10−10m=5000A∘The correct option is C.

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