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Question
In Young’s double slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ, is K units. Find out the intensity of light at a point where path difference is λ/3.
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Solution
We know
Phase difference `= ((2pi)/lambda) xx` path difference
At path difference λ
Phase difference ,`phi = (2pi)/lambda xx lambda = 2pi`
Intensity, `I = 4I_0 cos^2 phi/2`
or ,` K = 4I_0 cos^2 (2pi)/2` [given I = K at path difference λ]
or, `K = 4I_0`
or ,`I_0 = K/4`
Now, at path difference `= lambda/3`
`phi' = (2pi)/lambda xx lambda/3 = (2pi)/3`
Intensity , `I' =4I_0 cos^2 1/2 ((2pi)/3)`
0r, `I' = 4 xx K/4 cos^2 pi/3`
`I'=K/4`
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