# 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

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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