A ray of light is incident normally normallyh on one of the faces of a prism of apex angle `30^(@)` and refractive index `sqrt(2)`. The angle of deviation of the ray is `"________________"` degrees.

Options

A. `15^(@)`
B. `7.5^(@)`
C. `0^(@)`
D. `30^(@)`

Answer

A

Explanation

See figure for the ray diagram.

Light ray incident at point A on the prism goes un-deviated because it is incident normal to the surface. Angle of incidence at the point B becomes `30^(@)`. We can now apply Snell.s law to find angle of refraction r in air.
`mu sin theta="costant"`
`rArr" "sqrt2xxsin 30=1xxsinr`
`rArr" "sqrt2xx(1)/(2)=1xxsinr`
`rArr" "sin r=(1)/(sqrt2)`
`rArr" "r=45^(@)`
Hence, angle of deviation can be written as follows :
`delta=45-30=15^(@)`.
Hence, option (a) is correct.