A light ray enters a solid glass sphere of refractive index \mu =\sqrt{3} at an angle of  incidence 60o . The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degress) between the reflected and refracted rays at this surface is .........
Option: 1 30
Option: 2 60
Option: 3 45
Option: 4 90

Answers (1)

In the above figure

QR is reflected ray and QS is refracted ray. QT is tangent and OQ is normal. 

\begin{array}{l} \text { At P, } \mu \cdot \sin 60^{\circ}=\sqrt{3} \sin r \\ \Rightarrow \quad \frac{\sqrt{3}}{2}=\sqrt{2} \sin r \\ \Rightarrow \sin r=\frac{1}{2} \quad \therefore \quad r=30^{\circ} \end{array}

Similarly

At \ \ Q \\ \ \ \sqrt{3} \sin r=\operatorname{sini}^{\prime} \\ \therefore i^{\prime}=60^{\circ}

\therefore \ Angle \ between \ \ QR \ \ and \ \ QS\\ \Rightarrow(\angle \mathrm{RQS})=90^{\circ}

 

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