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  4. A ray of light falls on a transparent sphere with centre at C as shown in figure. The ray emerges from the sphere parallel to line AB. The refractive index of the sphere is

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Q. A ray of light falls on a transparent sphere with centre at $C$ as shown in figure. The ray emerges from the sphere parallel to line $AB$. The refractive index of the sphere isPhysics Question Image

Ray Optics and Optical Instruments

Solution:

Deviation by a sphere is $2(i-r)$
Here deviation $\delta=60^{\circ}=2(i-r)$
or $i-r=30^{\circ}$
$\therefore r=60^{\circ}-30^{\circ}=30^{\circ}$
$\therefore \mu=\frac{\sin i}{\sin r}=\frac{\sin 60^{\circ}}{\sin 30^{\circ}}=\sqrt{3}$