Question

What is the angle of the prism for which there will be no emergent ray from the prism if C is the critical angle ?

• A. 2C
• B. less than 2C
• C. more than 2C
• D. None of these

Answer 1

The correct option is C more than 2C

If the refracted ray inside the prism should undergo total internal reflection, then we have
$r_1+r_2=A$

If $r_2>C$, then the total internal reflection will occur
$\therefore r_{2min}=C$

Also we have $r_{1max}$ will also be $C$. This occurs when $i={90}^o$.

For critical transmission through the prism, the value of angle of prism $=r_{1max}+r_{2min}=2C$

Thus for the ray not to emerge the prism should have $A>2C$