Question

Find the angle of prism if the ray just fail to emerge from 2nd face When ray of light falls normallly on the face of prism of R.I. 1.5​

Answer 1

The angle of prism is 41.81 degrees.

Explanation:

For no emergence to be taken place, inside a prism, Total Internal Reflection (TIR) should take place at the second surface.  For TIR, at second surface, angle of refraction must be greater than critical angle. Angle of prism is related to refraction as,

                            $A>r_{1}+C$

Since, $r_{1}$ = C and $A \geq 2 C$

This implies $A \geq C$

                         $\sin A \geq \sin C$

                         $\sin A \geq \frac{1}{\mu}$

                         $\sin A \geq \frac{2}{3}$

when sin goes to other side become as sin inverse of value, and obtain the result as below,

                       $A=41.81^{\circ}$