Question

The critical angle of light going from medium A into medium B is $\theta$ . If the speed of light in medium A is $v$, then the speed of light in medium B is :

• A. $\frac{v}{\sin \theta }$
• B. $v\sin \theta$
• C. $\frac{v}{\tan \theta }$
• D. $v\tan \theta$

Answer 1

The correct option is A $\frac{v}{\sin \theta }$

For total internal reflection
$n_{A}sin\theta =n_B$

when $n_A=$ refractive index of medium A

$n_B=$ refractive index of medium B

$\frac{n_A}{n_B}=\frac{1}{sin\theta }$

by snell's law

$\frac{n_A}{n_B}=\frac{v_B\left(velocityinmediumB\right)}{v_A\left(velocityinmediumA\right)}$

$\frac{v_B}{v_A}=\frac{1}{sin\theta }$

$v_B=\frac{v_A}{sin\theta }$

$=\frac{v}{sin\theta }$