Question

The angle of the prism for which there is no emergent ray will be, if its critical angle is $i_c$

• A. greater than $i_c$
• B. less than $i_c$
• C. ${2i}_c$
• D. greater than ${2i}_c$

Answer 1

The correct option is D greater than ${2i}_c$

Applying snell's law at the two refracting surfaces,

$\sin i=\mu \sin r_1$

$\sin e=\mu \sin r_2$

Also $A=r_1+r_2$

For no emergent ray, $e={90}^{\circ }$

hence, $r_2=i_c$

Also for there to be no emergent ray in any case, $r_1$ can have the maximum value in the limiting case.

For this to happen, $i={90}^{\circ }$ in the case.

hence $r_1=i_c$

hence, $A>2i_c$