A light ray enters a solid glass sphere of refractive index μ = √(3)… | JEE Main 2020 (2 Sep, Shift 2)

Q40JEE Main 2020 · 2 SEP · SHIFT 2Difficult

Total Internal Reflection

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 ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 90

At entry: $\sin r = \frac{\sin 60^\circ}{\sqrt{3}} = \frac{1}{2} \Rightarrow r = 30^\circ$ .
Inside a sphere the chord makes equal angles with both radii, so incidence at the far surface is $30^\circ$ .
Reflected ray makes $30^\circ$ with the normal; refracted ray emerges at $60^\circ$ with the normal on the other side.
Angle between them $= 180^\circ - 30^\circ - 60^\circ = 90^\circ$

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Total Internal Reflection question from JEE Main 2020 (2 Sep, Shift 2)

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