Question

A ray of light is incident at the glass-water interface at an angle $i$ as shown in the figure. It finally emerges parallel to water-air interface. The value of $\mu_{g}$ would be (Refractive index of water, $\mu_{w}=\frac{4}{3}$ )

• A. $\frac{4}{3} \sin i$
• B. $\frac{1}{\sin i}$
• C. $\frac{4}{3}$
• D. none of these

Answer 1

Answer: (B)

Apply Snell's law at glass-water interface, we get
$\mu_{g} \sin i=\mu_{w} \sin r$
Apply Snell's law at water air-interface, we get
$\mu_{ air } \sin 90^{\circ}=\mu_{w} \sin r$

$\sin r=\frac{1}{\mu_{w}}=\frac{3}{4}$
Thus, $\mu_{g} \sin i=\frac{4}{3} \times \frac{3}{4}=1$
or $\mu_{g}=\frac{1}{\sin i}$