Question

A ray of light is incident at the glass-water interface at an angle $i$. It finally emerges parallel to the surface of water. Then, the value of ${\mu }_g$ (refractive index of glass) would be

• A. ${\mu }_g=\sin i$
• B. ${\mu }_g=\frac{1}{\sin i}$
• C. ${\mu }_g=\frac{3}{4\sin i}$
• D. None of the above

Answer 1

The correct option is B ${\mu }_g=\frac{1}{\sin i}$

Given: ${\mu }_w=4/3$

Applying Snell's law at point $\text{A}$,

${\mu }_g\sin i=\frac{4}{3}\sin r..........\left(1\right)$

Again applying Snell's law at $\text{B}$,

$\frac{4}{3}\sin r=1\times \sin 90{}^{\circ }$ [$\because {\mu }_{air}\approx 1$]

$\Rightarrow \sin r=\frac{3}{4}..........\left(2\right)$

Using eq.(2) in (1)

${\mu }_g=\frac{1}{\sin i}$
Hence, option $\left(b\right)$ is the correct answer.