A light of wavelength 500 nm is incident on a Young's double slit experiment. The distance
between slit and screen is D = 1. 8 m and distance between slits is d = 0.4 mm. If screen moves with a speed of 4 ms^-1, then with what speed first maxima will move? [AIIMS 2019]

Given, wavelength of light,
$\lambda$ = 500 nm = 5 X 10^-7 m
Distance between slit and screen,
D = 1.8m
Distance between two slits,
d = 0.4 mm = 4 x 10^-4 m
Velocity of screen  $=\frac{dD}{dt}=4{ \mathrm{ms}}^{-1}$

Speed of first maxima  $=\frac{d\beta }{dt}=?$

In Young's double slit experiment, fringe width,

$\beta =\frac{D\lambda }{d}$

Differentiating with respect to t, we get

$\frac{d\beta }{dt}=\frac{\lambda }{d}·\frac{dD}{dt}=\frac{5\times {10}^{-7}}{4\times {10}^{-4}}\times 4$

= 5 X 10^-3 ms^-1
= 5 mms^-1.