Question

A ray incident at an angle of incidence ${60}^{\circ }$ enters a glass sphere of refractive index $\mu =\sqrt{3}$. This ray is reflected and refracted at the farther surface of the sphere. The angle between reflected and refracted rays at this surface is

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is A

${90}^{\circ }$

$\mu =\frac{sini}{sinr}$
$\therefore sinr=\frac{sini}{\mu }$
$=\frac{sin{60}^{\circ }}{\sqrt{3}}=\frac{1}{2}$
$\therefore r={30}^{\circ }$
PC = QC
$\therefore \angle CPQ=\angle PQC=\angle r={30}^{\circ }$
Angle between reflected ray QR and refracted ray QS at the other face is ${180}^{\circ }–r–{60}^{\circ }$ or ${90}^{\circ }$ $(asr={30}^{\circ })$.