Question

A light ray enters a prism through the side PR. PQR is a cross section of the prism. The emergent ray lies
along the boundary OQ. P = 90° and PQ = PR. The ray diagram has been given.
What is the critical angle of the prism?

Answer 1

Answer:

The diagram is shown. The ray PQ enters the prism from the side AB, its angle of incidence is 0°. Thus it does not undergo any refraction. Its angle of refraction is also 0°. When this light ray reaches the base of the prism (BC), its angle of incidence (on the boundary BC) is 60° which is more than its critical angle (42°). Thus this incident light ray (QR) does not enter into the next medium, instead it undergoes total internal reflection. When this reflected light ray (RS) reaches the side AC, its angle of incidence is 0°. Again, it does not undergo any refraction, which causes the angle of emergence to become 0°.

Answer 2

Answer:

    The critical angle is $45$°.

Explanation:

   Given:

           ∠$p=90$°  and $PQ=PR$

    Therefore, ∠$R$ $=$ ∠$Q$.

            ∠$R +$∠$Q=90$°

            ∠$R$ $=$ ∠$Q$$=45$°

               ∠$OBR$$=90$°

    Therefore, ∠$BOR=45$°

                        ∠$BOC=45$°

    Hence, the critical angle is $45$°.