A ray of light from a denser medium strikes a rarer medium at angle of incidence i. The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are r & r' respectively. The critical angle is
Answer & explanation
Correct answer: option 1
Applying Snell’s Law for refraction,
$\frac{\sin i}{\sin r}=\frac{n_2}{n_1}$ …(1)
From the given condition, r + r' = 90
⇒ Sin r' = Cos r …(2)
Solution of (1) and (2) yields,
$\frac{\sin i}{\cos i}=\frac{n_2}{n_1}$ …(3)
According to the Law for refraction;
i = r …(4)
Using (3) and (4) we obtain
$⇒\tan i=\frac{n_2}{n_1}$ ….(5)
Also,
$\sin θ_c=\frac{n_2}{n_1}$, Using (5) we obtain $θ_c=\sin^{-1}(\tan i)=\sin^{-1}(\tan r)$