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Question

A monochromatic light source of wavelength λ is placed at S. Three slits S1,S2 and S3 are equidistance from the source S and the point P on the screen. S1PS2P=λ/6 and S1PS3P=2λ/3. If I be the intensity at P when only one slit is open, the intensity at P when all the three slits are open is?
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A
3I
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B
5I
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C
8I
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D
Zero
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Solution

The correct option is A 3I
Given, S1PS2P=λ6
Hence, phase difference between S1 and S2,ϕ=λ6×2πλ=π3
So intensity between S1 and S2 is,
I=Icos2(π6)2=3I4.........(i)
Given, S1PS3P=2λ3
Hence, phase difference between S1 and S3,ϕ=2λ3×2πλ=4π3
So intensity between S1 and S2 is,
I′′=Icos2(2π3)2=I4.........(ii)
The intensity at P when all the three slits are open is, III′′=3I

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