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.
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