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.

Answer

A, B, C

Explanation

The situation can be shown as in the figure.
Here, `60degree`,`A=30degree`,`delta=30degree`,`e=?`
We know that, `A+delta=i+e` ….(1)
Also, `A=r+r^(`)` ….(2)
From (1),
`e=A+delta-i=30degree+30degree-60degree=0`
As the angle of emergence (e) is 0, hence the emergent ray is normal to the face from which it emerges.
When `e=0`,`A=r=30degree`.
From Snell's law, refractive index of prism,
`mu=(sini)/(sinr)=(sin60degree)/(sin30degree)=((sqrt3)/(2))/((1)/(2))=sqrt3=1.732`.