Question

A ray of light is incident on a transparent glass slab of refractive index $1.62$ from the air with refractive index $1$. 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, r and r', respectively.
Now, as per the question 90 - r + 90 - r' = 90
$\Rightarrow$ r' = 90 - i (because i = r)
According to Snell's law,
1 sin i = $\mu$ sin r'
sin i = $\mu$ sin r'
sin i = $\mu$ sin (90 - i)
$\Rightarrow$ tan i = $\mu$
$i=ta{n}^{-1}\left(\mu \right)=ta{n}^{-1}\left(1.62\right)={58.3}^{\circ }$