In a Young's double slit experiment the intensity at the cetral maxima is I0. Find the intensity at a distance

B(beta)/4 from the central maxima where B(beta) is the fringe width.

Here,

Central maximum intensity = Io

β = λD/d

y = λD/4d

Now, in Young’s double slit experiment the path difference is given by

∆x = yd/D

=>  ∆x = (λD/4d)d/D = λ/4

Now phase difference corresponding to path difference λ/4

Will be φ = 2π/λ(λ/4) = π/2

Intensity due to interference is given by

I = I1 + I2 +2√(I1I2)cosφ

At central maximum φ = 0, I = Io, Let intensity of light from each slit I1 = I2 = Is

 => I0 = I1 + I2 +2√(I1I2)

=> Io = 4Is ---1.  

Now intensity at a distance β/4 is given by, cosφ = π/2

I = Is + Is +2√(I1I2)cos π/2

=> I = 2Is ---2

By 1 and 2.

I = Io/2

Thus intensity at β/4 is I0/2

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