The critical angle for light ray going from medium-1 to medium-2 is \( i_c \). What will be the speed of light in medium-2, if its value in medium-1 is u?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{u}{\sin i_c} \)
At the critical angle the refracted ray grazes the surface (angle of refraction \( 90^\circ \)), so Snell's law gives \( n_1\sin i_c = n_2\sin90^\circ \), that is \( \sin i_c = \frac{n_2}{n_1} \). The refractive index of a medium is \( n = \frac{c}{v} \), so \( \frac{n_2}{n_1} = \frac{v_1}{v_2} \).
\( \displaystyle \sin i_c = \frac{n_2}{n_1} = \frac{v_1}{v_2} = \frac{u}{v_2} \)
\( \displaystyle v_2 = \frac{u}{\sin i_c} \)
Since \( \sin i_c \lt 1 \), \( v_2 \gt u \): light travels faster in medium-2, which is the rarer medium, as total internal reflection requires.