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.

Answer 1

 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.