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

Refer to Fig.

Here, `i_(1) = 60^(@), A = 30^(@), delta = 30^(@),i_(2) = ?`
As `i_(1) + i_(2) = A + delta`
`:. 60^(@) + i_(2) = 30^(@) = 60^(@)`
`i_(2) = 0`
Hence emergent ray is normal to the surface,
When `i_(2) = 0, r_(2) = 0`
As `A = r_(1) + r_(2)`
`:. 30 = r_(1) + 0` or `r_(1) = 30^(@)`
Now `mu = (sin i_(1))/(sin r_(1)) = (sin 60^(@))/(sin 30^(@)) = (sqrt(3))/(2 xx 1//2) = sqrt(3)`