Question

Consider a usual set-up of Young's double slit experiment with slits of equal intensity as shown in the figure. Take 'O' as the origin and the Y axis as indicated. If the average intensity between y₁ = `(lambdaD)/(4d)` and y₂ = `(lambdaD)/(4d)` equals n times the intensity of maximum, then n equal is (take average over phase difference) ______.

 

विकल्प

• `1/2(1  + 2/pi)`

• `2(1 + 2/pi)`

• `(1 + 2/pi)`

• `1/2(1 - 2/pi)`

Answer 1

Consider a usual set-up of Young's double slit experiment with slits of equal intensity as shown in the figure. Take 'O' as the origin and the Y axis as indicated. If the average intensity between y₁ = `(lambdaD)/(4d)` and y₂ = `(lambdaD)/(4d)` equals n times the intensity of maximum, then n equal is (take average over phase difference) `underlinebb(1/2(1  + 2/pi))`.

Explanation:

Phase difference corresponding to `y_1  = (-pi)/2` and that for `y_2 = +pi/2`

∴ Average intensity between y₁ and y₂,

= `1/piint_{-pi/2}^{pi/2}I_{max} cos^2(Phi/2)dPhi`

= `I_{max} ((pi + 2))/(2pi)`

Hence required ratio = `1/2(1  + 2/pi)`