Question

Let the refractive index of a denser medium with respect to a rarer medium be $n_{12}$ and its critical angle be $\theta_C$. At an angle of incidence $A$ when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is $90^{\circ}$. Angle $A$ is given by :

• A. $\frac{1}{\cos^{-1} \left(\sin \theta_{C}\right)}$
• B. $\frac{1}{\tan^{-1} \left(\sin \theta_{C}\right)}$
• C. $\cos^{-1} (\sin \theta_C)$
• D. $\tan^{-1} (\sin \theta_C)$

Answer 1

Answer: (D)

$\mu = \frac{\mu_{R}}{\mu_{D}} = \frac{sin_{c}}{sin90^{\circ}}$
$\frac{\mu_{R}}{\mu_{D}} = sin \,i_{i}$
$\mu = \frac{\mu_{R}}{\mu_{D}} = \frac{sin A}{sinr}$
$= \frac{sinA}{sin\left(90 - A\right)} = \frac{sinA}{cosA}$
$\frac{\mu_{R}}{\mu_{D}} = tan \,A$
$tan \,A = sin \theta_{C}$
$A = tan^{-1} \left(sin \,\theta_{C}\right)$