Question

What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

• A. $n<cosec\left(\frac{A}{2}\right)$
• B. $n<\sec \left(\frac{A}{2}\right)$
• C. $n>\sec A$
• D. $n>cosec\left(\frac{A}{2}\right)$

Answer 1

The correct option is D $n>cosec\left(\frac{A}{2}\right)$

The light has to do total internal reflection at the second face so that it cannot come out of the prism.

Condition for total internal reflection $\sin r>\frac{1}{n}$

But $A=r+r=2r$

$⟹r=\frac{A}{2}$

Thus we get $\sin \frac{A}{2}>\frac{1}{n}$

$⟹n>cosec\frac{A}{2}$