Question

The critical angle of a medium B with respect another medium A is 45${}^{\circ }$ and the critical angle of a medium C with respect the medium B is 30${}^{\circ }$. The critical angle of medium C with respect to A is :

• A. Less than 30${}^{\circ }$
• B. Greater than 30${}^{\circ }$
• C. 30${}^{\circ }$
• D. Cannot be determined

Answer 1

The correct option is A Less than 30${}^{\circ }$

${\mu }_{B}sin{45}^{\circ }={\mu }_A$

${\mu }_{C}sin{30}^{\circ }={\mu }_B$

${\mu }_{C}sin30sin45={\mu }_A$

${\mu }_C\frac{1}{2\sqrt{2}}=\mu A$

$\therefore criticalangle=si{n}^{-1}\left(\frac{1}{2\sqrt{2}}\right)<{30}^{\circ }$