Question

Velocity of light in glass is $2\times {10}^{8}m{s}^{-1}$ and in air is $3\times {10}^{8}m{s}^{-1}$. If the ray passes through glass to air, calculate the value of critical angle.

• A. ${40}^{\circ }$
• B. ${42}^{\circ }$
• C. ${45}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is B

${42}^{\circ }$

Velocity of light in glass (n_g) = $2\times {10}^{8}m{s}^{-1}$
Velocity of light in air (n_a) =$3\times {10}^{8}m{s}^{-1}$
Critical angle is found from the formula:
$\frac{n_a}{n_g}=\frac{1}{sin\left(i_c\right)}$
$\frac{1}{sin\left(i_c\right)}=\frac{n_a}{n_g}=\frac{3\times {10}^8}{2\times {10}^8}=1.5$
$sin{i}_c=\frac{1}{1.5}\therefore i_c=si{n}^{-1}\left(\frac{1}{1.5}\right)={42}^{\circ }$