A ray of light is incident at an angle of `60^@` on the face of a prism having refracting angle `30^@.` The ray emerging out of the prism makes an angle `30^@` with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of prism.

Explanation

The angle of deviation
`delta=(i_(1)+i_(2))-A`
Here, `delta=30^(@)`,
`i_(1)=60^(@)`
`A=30^(@)`
Hence `30^(@)=60^(@)+i_(2)-30^(@)=30^(@)+i_(2)`
`rArr i_(2)=0`
The angle of emergence is zero. This means that the emergent ray is perpendicular to the second face. Since `i_(2) = 0`, the anlge of incidence at the second face is zero.
`:. r_(2)=0`
Now, `r_(1)+r_(2)=A`
or, `r_(1)=A=30^(@)`
We know,
`mu=(sin i_(1))/(sin r_(1))=(sin 60^(@))/(sin 30^(@))=(sqrt(3)//2)/(1//2)`
`sqrt(3)=1.732`