Question

A ray of light is incident normally on one face of ${30}^{\circ }-{60}^{\circ }-{90}^{\circ }$ prism of refractive index 5/3 immersed in water of refractive index 4/3 as shown in figure .

• A. The exit angle ${\theta }_2$ of the ray is ${sin}^{-1}$ (5/8)
• B. The exit angle ${\theta }_2$ of the ray is ${sin}^{-1}$ $\left(5/4\sqrt{3}\right)$
• C. Total internal reflection at point P ceases if the refractive index of water is increased to $5/4\sqrt{3}$ by dissolving some substance .
• D. Total internal reflection at point P ceases if the refractive index of water is increase to 5/6 by dissolving some substance .

Answer 1

The correct option is A The exit angle ${\theta }_2$ of the ray is ${sin}^{-1}$ (5/8)

Given,

The refractive index pf prism is ${\mu }_p=\frac{5}{3}$ and the refractive index of water is ${\mu }_w=\frac{4}{3}$.

From the figure it can be seen that ${\theta }_1={60}^{\circ }$

Applying Snell’s law

${\mu }_p\sin {30}^{\circ }={\mu }_w\sin {\theta }_2$

$\frac{5}{3}\sin {30}^{\circ }=\frac{4}{3}\sin {\theta }_2$

$\frac{5}{3}\times \frac{1}{2}=\frac{4}{3}\sin {\theta }_2$

$\sin {\theta }_2=\frac{3}{4}\times \frac{5}{3}\times \frac{1}{2}$

$\sin {\theta }_2=\frac{5}{8}$

${\theta }_2={\sin }^{-1}\left(\frac{5}{8}\right)$

Hence the exit angle of the ray is ${\theta }_2={\sin }^{-1}\left(\frac{5}{8}\right)$ .