Question

Figure shows plane waves refracted from air to water using Huygens' principle. $a,b,c,d$ and $e$ are the lengths on the diagram. The refractive index of water with respect to air is

• A. $\frac{a}{e}$
• B. $\frac{b}{e}$
• C. $\frac{b}{d}$
• D. $\frac{d}{b}$

Answer 1

The correct option is C $\frac{b}{d}$


According to the Huygens' principle

$\Rightarrow \frac{\sin i}{\sin r}=\frac{{\mu }_w}{{\mu }_a}$

$\Rightarrow \frac{b/c}{d/c}=\frac{{\mu }_w}{{\mu }_a}$

Since medium $1$ is air ${\mu }_a\simeq 1$

$\therefore {\mu }_2=\frac{b}{d}$

Hence, option $\left(\text{C}\right)$ is correct.