A parallel beam of light of wavelength `lambda` passes through a slit of width d. The transmitted light is collected on a screen D aways `(D gt gt d)`. Find the distance between the two second order minima.

Options

A. `(D lambda)/(d)`
B. `(D lambda)/(2d)`
C. `(2D lambda)/(d)`
D. `(4D lambda)/(d)`

Answer

D

Explanation

`tan theta = (x)/(2D)`
For second minima
`sin theta = (2 lambda)/(d) ~~ tan theta`
`rArr (x)/(2D) = (2 lambda)/(d)`
`rArr x = (4 lambda D)/(d)`