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

Since the emergent ray makes `30^(@)` with the incident ray, the angle of deviation = `30^(@)`
we have `i+e=A+delta`
or `60^(@)+e=30^(@)+30^(@)`
or e = 0
`therefore` The emergent ray is perpendicular to the face through which it emerges.
Also r + r. = A
`rArrr=A=30^(@)" "[becausel=0rArrr.=0]`
`thereforemu=sini/sinr=(sin60^(@))/(sin30^(@))=sqrt3/2xx2=sqrt3`