In Young's double-slit experiment the angular width of a fringe formed on a distant screen is `1^(@)`. The wavelength of light used is `6000 Å`. What is the spacing between the slits?

Options

A. 1 mm
B. 0.05 mm
C. 0.03 mm
D. 0.01 mm

Answer

C

Explanation

In Young's double slit experiment
`sin theta =theta = (y//D)` , so `Deltatheta = (Deltay//D)`
Hence, angular fringe with `theta_0 =Deltatheta`
(with `Deltay=beta` ) will be
`theta_0=beta/D=(Dlambda)/d xx 1/D =lambda/d`
Here `theta_0 =1^@ = (pi//180)` rad and `lambda` = 6000 Å = `6 xx 10^(–7)` m
So `d=lambda/theta_0 =180/pixx6xx10^(-7)=3.44xx10^(-5)` m
= 0.0344 mm