Answer to Question #117939 in Optics for Samaja

Question

A ray of light is incident on a plane surface of refractive index√3 at a certain angle it is found that the reflected and refracted rays are perpendicular to each other then the angle of incidence is ?

Answer 1

Let the angle of incidence, angle of reflection, and angle of refraction be i , r and r′, respectively.

Now, as per the equation

$(90^∘−r)+(90^∘−r^′)=90^∘$

$r^′=(90^∘−i)$  (because i=r, in case of reflection according to Snell's law, 1 sin i =μsinr′)

$or\ \sin i= μ \sin r^′$

$\sin i =μ\sin(90∘−i)⇒\tan i=μ$

$i=\tan^{−1}μ=tan^{−1}√3=60^∘$