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 origin and the Y axis as indicated. If average intensity between y₁ = $\frac{\lambda D}{4d}$ and y₂ = $\frac{\lambda D}{4d}$ equals n times the intensity of maximum, then n equal is (take average over phase difference) –

• A. $\frac{1}{2}\left( 1 + \frac{2}{\pi} \right)$
• B. 2 $\left( 1 + \frac{2}{\pi} \right)$
• C. $\left( 1 + \frac{2}{\pi} \right)$
• D. $\frac{1}{2}\left( 1 - \frac{2}{\pi} \right)$

Answer 1

Answer: (A)

$\frac{1}{2}\left( 1 + \frac{2}{\pi} \right)$

Answer 2

Phase difference correspnding to y₁ = $\frac{–\pi}{2}$ and that for y₂ = + $\frac{\pi}{2}$

\ Average intensity between y₁ and y₂

= $\frac{1}{\pi}$ $\int_{- \pi/2}^{\pi/2\int}{I\cos^{2}\left( \frac{\varphi}{2} \right)}_{\max}$

= I_max $\frac{(\pi + 2)}{2\pi}$

Hence required ratio = $\frac{1}{2}$ $\left( 1 + \frac{2}{\pi} \right)$