Physics - Geometrical Optics Question with Solution | TestHub

Velocity of light in diamond, $v_d=\frac{5}{12}c$

Refractive index of diamond, ${\mu }_d=\frac{c}{v_d}=\frac{12}{5}$

Velocity of light in water, $v_w=\frac{3}{4}c$

Refractive index of water, ${\mu }_w=\frac{c}{v_w}=\frac{4}{3}$

Applying Snell's law for light travelling from water to diamond:

${\mu }_w\sin i={\mu }_d\sin r$

$\frac{4}{3}\sin i=\frac{12}{5}\sin 30^{\circ }$

$\frac{4}{3}\sin i=\frac{12}{5}\times \frac{1}{2}$

$\frac{4}{3}\sin i=\frac{6}{5}$

$\sin i=\frac{6}{5}\times \frac{3}{4}=\frac{9}{10}$

$i={\sin }^{-1}\left(\frac{9}{10}\right)$

Answer: ${\sin }^{-1}(9/10)$