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Question
In a Young’s double slit experiment, the path difference at a certain point on the screen between two interfering waves is `1/8`th of the wavelength. The ratio of intensity at this point to that at the centre of a bright fringe is close to ______.
Options
0.80
0.74
0.94
0.85
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Solution
In a Young’s double slit experiment, the path difference at a certain point on the screen between two interfering waves is `1/8`th of the wavelength. The ratio of intensity at this point to that at the centre of a bright fringe is close to 0.85.
Explanation:
Δx = `λ/8`
Path difference `Δphi = (2π)/λ xx Δx = (2π)/λ xx λ/8 = π/4`
`I = I_0 cos^2 ((Δphi)/2) = I_0 cos^2(π/8)`
`I/I_0 = cos^2(π/8)` = 0.85
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