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, angle of reflection and angle of refraction be i, r and r', respectively.
Now, as per the question 90 - r + 90 - r' = 90
$\Rightarrow$ r' = 90 - i(because i = r)

In case of reflection according to Snell's law, 1 sin i = $\mu$ sin r'
or sin i = $\mu$ sin r' or sin i = $\mu$ sin (90 - i)
$\Rightarrow$ tan i = $\mu$ or $i=ta{n}^{-1}\left(\mu \right)=ta{n}^{-1}\left(1.62\right)={58.3}^{\circ }$