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Question

The path difference between two interfering waves at a point on the screen is λ6from central maximum. The ratio of intensity at this point and that at the central fringe will be:

A
0.75
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B
7.5
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C
85.3
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D
853
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Solution

The correct option is A 0.75
At a point with phase difference θ the intensity is given by I=2a2(1+cosθ)
The maximum intensity is given by 4a2
For path difference λ/6, the phase difference is given by:
θ=2πΔx/λ=2π/6=π/3
Thus the ratio is 2a2(1+cosθ)4a2=1+cosθ2
=1+1/22=0.75

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