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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 that path difference is related to the phase difference 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 l
then `l_(0)=4lcos^(2)((4pi)/2)=4l`
hence `l=(l_(0))/4`
Now at point where `phi=(2pi)/3`
`l'=4lcos^(2)((2pi)/(3xx2))`
`l'=4lcos^(2)((pi)/3)=l=(l_(0))/4`
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