Two thin parallel slits are made in on opaque sheet of film when a monochromatic beam of light is shonw through then at normal incidence. The first bright fringes in the transmitted light occur at `+- 45^(@)` with the original direction of the ligth beam on a distant screen when the apparatus is in air. When the apparatus is immersed in a liquid, the same bright fringe now occur at `+- 30^(@)`. The index of refraction of the liquid is

Options

A. `sqrt 2`
B. `sqrt 3`
C. `(4)/(3)`
D. `(3)/(2)`

Answer

a

Explanation

`d sin theta_(1) - n lambda_(1) , d sin theta_(2) = n lambda_(2)`
`(sin theta_(1))/(sin theta_(2)) = (lambda_(1))/(lambda_(2)) = mu`
`mu = (sin theta_(1))/(sin theta_(2)) = (sin 45^(@))/(sin 30^(@)) = sqrt 2`