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)

$\mu =\frac{{\mu }_R}{{\mu }_D}=\frac{si{n}_c}{sin90^{\circ }}$
$\frac{{\mu }_R}{{\mu }_D}=sin{i}_i$
$\mu =\frac{{\mu }_R}{{\mu }_D}=\frac{sinA}{sinr}$
$=\frac{sinA}{sin\left(90-A\right)}=\frac{sinA}{cosA}$
$\frac{{\mu }_R}{{\mu }_D}=tanA$
$tanA=sin{\theta }_C$
$A=ta{n}^{-1}\left(sin{\theta }_C\right)$