**In a Young's double slit experiment the intensity at the cetral maxima is I _{0}. Find the intensity at a distance**

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

Here,

Central maximum intensity = I_{o}

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 = I_{1} + I_{2} +2√(I_{1}I_{2})cosφ

At central maximum φ = 0, I = I_{o}, Let intensity of light from each slit I_{1} = I_{2 }= I_{s}

=> I_{0} = I_{1} + I_{2} +2√(I_{1}I_{2})

=> I_{o} = 4I_{s }---1.

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

I = I_{s} + I_{s} +2√(I_{1}I_{2})cos π/2

=> I = 2I_{s} ---2

By 1 and 2.

I = I_{o}/2

Thus intensity at β/4 is I_{0}/2

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