In two separate set-ups of the Young's double slit experiment, fringes of equal width are observed when lights of wavelength in the ratio of `1:2` are used. If the ratio of the slit separation in the two cases is `2:1`, the ratio of the distance between the plane of the slits and the screen in the two set-ups are

Options

A. `1:4`
B. `1:1`
C. `2:1`
D. `4:1`

Answer

D

Explanation

`X=(lamda_(1)D_(1))/(d_(1))=(lamda_(2)D_(2))/(d_(2))`
`therefore (D_(1))/(D_(2))=(lamda_(2)d_(1))/(lamda_(1)d_(2))=(2)/(1)xx(2)/(1)=(4)/(1)`
`therefore D_(1):D_(2)=4:1`