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

Options

A. `1.732`
B. `1.414`
C. `1.5`
D. `1.33`

Answer

A

Explanation

Here, `i=60^(@), A=30^(@), delta=30^(@)`

As `i+e=A+delta`
`e=A+delta-i`
`=30^(@)+30^(@)-60^(@)`
`e=0^(@)`
Hence emergent ray is normal to the surface.
`e=0^(@)impliesr_(2)=0^(@)`
As `r_(1)+r_(2)=A`
`:.r_(1)=A-r_(2)=30^(@)-0^(@)=30^(@)`
`mu=(sini)/(sinr_(1))=(sin60^(@))/(sin30^(@))=(sqrt(3))/(2)xx(2)/(1)=sqrt(3)=1.732`