Question

A ray of light falls on a transparent glass plate($\mu =\sqrt{3}$ ) part of it is reflected and part is refracted. If the reflected and refracted rays are perpendicular to each other then the angle of incidence is

• A. 30${}^{\circ }$
• B. 45${}^{\circ }$
• C. 60${}^{\circ }$
• D. 90${}^{\circ }$

Answer 1

The correct option is C 60${}^{\circ }$

Let angle of incidence be $i$

Angle of reflection = $r$

Angle of redfraction calculation: $\mu sinr=1\times sini$

= >$sinr=\frac{sini}{\mu }$

=> $r=si{n}^{-1}\left(\frac{sini}{\sqrt{3}}\right)$

Angle between reflected and redfracted ray = $180-i-r={90}^{\circ }$

=> $180-i-si{n}^{-1}\left(\frac{sini}{\mu }\right)={90}^{\circ }$

=> $i+si{n}^{-1}\left(\frac{sini}{\sqrt{3}}\right)={90}^{\circ }$

=> i = ${60}^{\circ }$

$Answer:C){60}^{\circ }$