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 $ \theta $ for the following refraction?

• 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

Answer: (B)

Using the formula
$\mu_{\text {prism }}=\frac{\mu_{\text {liquid }}}{\mu_{\text {prism }}}=\frac{1.32}{1.56}=\frac{11}{13}\,\,\,\,...(1)$
Now the condition for total internal reflection, occur when $\sin \theta \geq \mu$
So, $\sin \theta \geq \frac{11}{13}$