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. $A \geqslant 2C$

Answer 1

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).

Additional Information:
The two plane surfaces of the prism are called Refracting faces and angle between two refracting faces is called angle of the prism.
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.

Note: The sum of angle of prism and angle of deviation is equal to the sum of the angle of incidence and the angle of emergence.