Question

A ray of light is incident on a transparent glass slab of refractive index 1.62. If the reflected and refracted rays are mutually perpendicular, what is the angle of incidence?

• A. $ta{n}^{-1}\left(1.62\right)$
• B. $co{t}^{-1}\left(1.62\right)$
• C. $si{n}^{-1}\left(1.62\right)$
• D. $co{s}^{-1}\left(1.62\right)$

Answer 1

The correct option is A $ta{n}^{-1}\left(1.62\right)$

Let the angle of incidence, the angle of reflection and angle of refraction be $i,rand{r}^{\prime }$, respectively.

Now, as per the question $90-r+90-r^{\prime }=90$

$\Rightarrow r^{\prime }=90-i(becausei=r)$

In case of reflection according to Snell's law,

$\Rightarrow 1\times sin\left(i\right)=\mu sin\left(r^{\prime }\right)\Rightarrow sin\left(i\right)=\mu .sin\left(r^{\prime }\right)orsin\left(i\right)=\mu .sin(90-i)$

$\Rightarrow tan\left(i\right)=\mu ori=ta{n}^{-1}\left(\mu \right)=ta{n}^{-1}\left(1.62\right)={58.3}^{\circ }$