Question 108 of 295

A light ray enters a solid glass sphere of refractive index $\mu =\sqrt{3}$ at an angle of incidence $60^{\circ}$. 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 _____________.

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Answer: 90

Apply Snell's law at S_
$1\sin 60^{\circ}=\sqrt{3}\sin r$
$\sin r=\dfrac{1}{2}$
$r=30^{\circ}$
from geometry
${r}^{'}=30^{\circ}$
Again apply snell's law on ${S}_{2}$
$\sqrt{3}{sinr}^{'}=1sine$
$\dfrac{\sqrt{3}}{2}=sine$
$∴e=60^{\circ}$
from geometry
${r}^{'}+\theta +e=180^{\circ}$
$\theta =90^{\circ}$