Question

The refractive index of the material of the prism and liquid are $1.56$ and $1.32$ respectively. What will be the value of θ?

• A. $sin\theta \ge \frac{13}{11}$
• B. $sin\theta \ge \frac{11}{13}$
• C. $sin\theta \ge \frac{\sqrt{3}}{2}$
• D. $sin\theta \ge \frac{1}{\sqrt{2}}$

Answer 1

The correct option is B

$sin\theta \ge \frac{11}{13}$

For total internal reflection from surface BC

$\theta \ge C\Rightarrow sin\theta \ge sinC$

$\Rightarrow sin\theta \ge \left(\frac{1}{\mu }\right)$

$\Rightarrow sin\theta \ge \left(\frac{{\mu }_{Liquid}}{{\mu }_{Prism}}\right)$

$sin\theta \ge \left(\frac{1.32}{1.56}\right)\Rightarrow sin\theta \ge \frac{11}{13}$