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Question
The intensity at the central maxima in Young’s double slit experimental set-up is I0. Show that the intensity at a point where the path difference is λ/3 is I0/4.
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Solution
Intensity at a point is given by,
I = 4I’ cos2∅/2
Where, ∅ = phase difference
I’ = intensity produced by each one of the individual sources.
At central maxima, ∅ = 0,
I = I0 = 4I
`or, I'=I_0 /4 .... (1)`
At path difference `= lambda/3,`
Phase difference,`phi =(2pi)/lambda xx `path difference
`(2pi)/lambda xx lambda / 3 = (2pi)/3`
Now, intensity at this point,
Hence proved.
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