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In a Young's double slit set up using mo...

In a Young's double slit set up using monochromatic light of wavelength `lambda` the intensity of light at a point, where path difference is `2lambda` is found to be `I_(0)` What will be the intensity at a point when path different is `lambda//3` ?

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We know according to the relation , `phi=(2pix)/lambda`
Now, phase difference, where path difference is equal to `lambda//3`
is equal to `phi=(2pi)/lambda xx lambda/3=(2pi)/3`
Also, at the point, where path difference `=2lambda`
Phase difference will be `(2pi)/lambda xx2lambda=4pi`
Let individual source intensity be I
Then, `I_(0)=4I cos^(2)(4pi)/2=4I`
Hence, `I=I_(0)/4`
Now, at point, where `phi=(2pi)/3`
`rArr I' = 4I cos^(2)(2pi)/(3xx2)`
`I' = 4I cos^(2)(pi/3)=I=I_(0)/4`
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