Question

A ray of light is incident at `60^(@)` on one face of a prism of angle `30^(@)` and the emergent ray makes `30^(@)` with the incident ray. The refractive index of the prism is
A. `1.732`
B. `1.414`
C. `1.5`
D. `1.33`

Answer 1

Correct Answer - A

Here `i = 60^(@), A = 30^(@), delta = 30^(@)`
As `i + e = A + delta`
`e = A + delta - i = 30^(@) + 30^(@) - 60^(@) - 0^(@)`
Hence emergent ray is normal to the surface.

`e = 0^(@) rArr r_(2) = 0^(@)`
As `r_(1) r_(2) = A`
`:. r_(1) = A - r_(2) = 30^(@) - 0^(@) = 30^(@)`
`mu = (sin 60^(@))/(sin 30^(@)) = (sqrt(3))/(2) xx (2)/(1) = sqrt(3) = 1.732`