Question

A ray of light propagates from glass (refractive index = 3/2) to water (refractive index = 4/3).The value of the critical angle:

• A. ${\sin }^{-1}\left(1/2\right)$
• B. ${\sin }^{-1}\left(\frac{\sqrt{8}}{9}\right)$
• C. ${\sin }^{-1}\left(8/9\right)$
• D. ${\sin }^{-1}\left(5/7\right)$

Answer 1

The correct option is C ${\sin }^{-1}\left(8/9\right)$

$\begin{array}{c}i={\theta }_c\\ {\upsilon }_1\mathrm{sini}={\upsilon }_2\sin r\\ \frac{3}{2}\times \sin {\theta }_c=\frac{4}{3}\times \sin 90\\ \frac{3}{2}\sin {\theta }_c=\frac{4}{3}\\ \sin {\theta }_c=\frac{4}{3}\times \frac{2}{3}=\frac{8}{9}\\ {\theta }_c={\sin }^{-1}\left(\frac{8}{9}\right)\end{array}$