The reflected and the refracted rays are perpendicular to each other when light is incident on a transparent denser medium having refractive index $\sqrt{3}$. The angle of incidence is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 60°
Given:
Refractive index of medium, $\mu = \sqrt{3}$
Condition: Reflected ray and refracted ray are perpendicular to each other.
Hence, angle between them = $90^\circ$.
By Snell’s law:
$\mu = \frac{\sin i}{\sin r}$
Also, from geometry of the condition:
$i + r = 90^\circ$
Substitute $r = 90^\circ - i$ in Snell’s law:
$\mu = \frac{\sin i}{\sin (90^\circ - i)} = \frac{\sin i}{\cos i} = \tan i$
Therefore, $\tan i = \sqrt{3}$
$i = 60^\circ$
Final Answer: $i = 60^\circ$