A ray of light is incident at an angle of 60^@ on one face of prism which has an angle of 30^@. The ray emerging out of the prism makes an angle of 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 the prism?

A ray of light is incident at an angle of 60^@ on one face of prism wh

1.	A ray of light is incident at an angle of 60^@ on one face of prism which has an angle of 30^@. The ray emerging out of the prism makes an angle of 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 the prism?
Answer» Solution :According to given problem `A=30^@, i_1=60^@ and DELTA=30^@` and as in prism, `delta=(i_1+i_2)-A` `30^@=(60^@+i_2)-30^@ i.e., i_2=0^@` So the emergent RAY is perpendicular to the FACE from WHICHIT EMERGES Now as `i_2=0,r_2=0` But as `r_1+r_2=A, r_1=A=30^@` So at first face `1 sin 60^@=mu sin 30^@` i.e. `mu=sqrt3`