Light is incident on a substance of refractive index `sqrt(2)` at an angle of `45^(@)`. What is the ratio of width of beam in air to the medium ?

Options

A. `sqrt(3) : sqrt(2)`
B. `1 : sqrt(15)`
C. `1:2sqrt(2)`
D. `sqrt(2) : sqrt(3)`

Answer

D

Explanation

`mu = sqrt(2), I = 45, (AB)/(CD) = ?`
`mu = (sin i)/(sin r)`
`sin r = (sin i)/(mu) = (sin 45)/(sqrt(2)) = (1)/(2)`
`:. r = 30^(@)`
Now `(AB)/(CD) = (cos i)/(cos r) = (cos 45)/(cos 30)`
`= ((1)/sqrt(2))/((sqrt(3))/(2)) = (1)/(sqrt(2)) xx (2)/(sqrt(3)) = (sqrt(2))/(sqrt(3))`