JEE PYQ: Ray Optics Question 15
Question 15 - 2020 (02 Sep Shift 2)
A light ray enters a solid glass sphere of refractive index $\mu = \sqrt{3}$ at an angle of incidence 60$°$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is _________.
Show Answer
Answer: (90)
Solution
In the figure, $QR$ is the reflected ray and $QS$ is refracted ray. $CQ$ is normal. Apply Snell’s law at $P$: $1 \sin 60° = \sqrt{3} \sin r$ $\Rightarrow \sin r = \frac{1}{2} \Rightarrow r = 30°$ From geometry, $CP = CQ$ $\therefore r’ = 30°$ Again apply Snell’s law at Q, $\sqrt{3} \sin r’ = 1 \sin e$ $\Rightarrow \frac{\sqrt{3}}{2} = \sin e \Rightarrow e = 60°$ From geometry $r’ + \theta + e = 180°$ (As angles lies on a straight line) $\Rightarrow 30° + \theta + 60° = 180° \Rightarrow \theta = 90°$
BETA
