Question

# If the critical angle for the medium of prism is C and the angle of prism is A, then there will be no emergent ray when-A. $A < 2C$B. $A = 2C$C. $A > 2C$D. $A \geqslant 2C$

Hint: Limiting value of angle of prism is equal to twice the critical angle.

Complete step by step solution:
It is given that
Angle of Prism $= A$
Critical angle $= C$
We know that Limiting value of the angle of the prism is equal to twice the critical angle.
${A_{max}} = 2C$
So no emergent ray will be there when $A > 2C$

So, the correct option is (C).

Another way to understand it is that we know $r1 + r2 = A$, where $r1$ is angle of incidence at entrance and $r2$ is angle of emergence.
To be able to enter the prism, $r1$ should be less than or equal to C.
Now for exit, $r2$ should be less than or equal to C. Combining these two statements, we conclude that if $r1 + {\text{ }}r2{\text{ }} > {\text{ }}C$, then there will be no emergent ray.