Question

Velocity of light in glass is 2 × 10⁸ m/s and in air is 3 × 10⁸ m/s. If the ray of light passes from glass to air, calculate the value of critical angle.

Answer 1

 Given:

\[\text { Velocity of light in air }, v_a = 3 \times {10}^8 m s^{- 1} \]

\[\text { Velocity of light in glass}, v_g = 2 \times {10}^8 m s^{- 1} \]

\[\text { The refractive index of glass is given by }\]

\[ \mu_g = \frac{c}{v_g}\]

\[\text { where c is speed of light in vacuum }\]

\[\text { The refractive index of air is given by }\]

\[ \mu_a = \frac{c}{v_a}\]

\[ \therefore\text {  The refractive index of glass w . r . t air will be }\]

\[ {}^a \mu_g = \frac{\mu_g}{\mu_a}\]

\[ \Rightarrow^a \mu_g = \frac{v_a}{v_g} = \frac{3 \times {10}^8}{2 \times {10}^8} = 1 . 5\]

\[\text { We know } \]

\[^a \mu_g = \frac{1}{\sin C}\]

\[\text { where C is the critical angle for the interface }\]

\[ \Rightarrow \frac{1}{\sin C} = 1 . 5\]

\[ \Rightarrow \sin C = \frac{1}{1 . 5}\]

\[ \Rightarrow C = \sin^{- 1} (0 . 66)\]

\[ \Rightarrow C = 41 . 3°\]

\[ \therefore \text { Critical angle } C = 41 . 3°\]