Question

A ray of light is incident on a glass slab making an angle of ${60}^{\circ }$ with the surface. Calculate the angle of refraction in glass and the velocity of light in glass if the refractive index of glass and the velocity of light in air are $1.5$ and $3\times {10}^{8}m/s$ respectively

• A. ${39}^{\circ }{28}^{\prime };2\times {10}^{9}m/s$.
• B. ${19}^{\circ }{28}^{\prime };2\times {10}^{8}m/s$.
• C. ${19}^{\circ }{28}^{\prime };2\times {10}^{18}m/s$.
• D. ${29}^{\circ }{28}^{\prime };2\times {10}^{8}m/s$.

Answer 1

The correct option is B ${19}^{\circ }{28}^{\prime };2\times {10}^{8}m/s$.

$i={90}^{\circ }-{60}^{\circ }={30}^{\circ }$

$\eta =\frac{\sin i}{\sin r}$

$1.5=\frac{\sin {30}^{\circ }}{\sin r}$

$\sin r=\frac{1}{2\ast 1.5}$

$r={19}^{\circ }{28}^{‘}$

${\eta }_{glass}=\frac{v_{air}}{v_{glass}}$

$1.5=\frac{3\ast {10}^8}{v_{glass}}$

$v_{glass}=2\ast {10}^{8}m/s$

Hence option 'B' is correct.