Question

A ray of light is incident normally on one face of a prism as shown in figure. The refractive index of the material of the prism is $\frac{5}{3}$ and the prism is immersed in water of refractive index $\frac{4}{3}$ then

• A. The angle of emergence ${\Theta }_2$ of the ray is $si{n}^{-1}\left(\frac{5}{8}\right)$
• B. The angle of emergence ${\Theta }_2$ of the ray is $si{n}^{-1}\left(\frac{5}{4\sqrt{3}}\right)$
• C. The angle of emergence ${\Theta }_2$ of the ray is $si{n}^{-1}\left(\frac{7}{3\sqrt{4}}\right)$
• D. Total internal reflection will not occur at P if the refractive index of water increases to a value greater than $\frac{5}{2\sqrt{3}}$ by dissolving some substance

Answer 1

Answer: (A), (D)

The angle of emergence ${\Theta }_2$ of the ray is $si{n}^{-1}\left(\frac{5}{8}\right)$
Total internal reflection will not occur at P if the refractive index of water increases to a value greater than $\frac{5}{2\sqrt{3}}$ by dissolving some substance

Initially at P, there is TIR, There force at Q (snells law)

$\frac{5}{3}sin{30}^0=\frac{4}{3}sin{\Theta }_2$

$\Rightarrow sin{\Theta }_2=\frac{5}{8}\Rightarrow {\Theta }_2=si{n}^{-1}\left(\frac{5}{8}\right)$

If ${\mu }_w>\frac{5}{2\sqrt{3}}\Rightarrow sinC>\frac{5/2\sqrt{3}}{2/3}\Rightarrow C>{60}^0$

Therefore, now TIR will not occur at P