Question

If $AB$ is the wavefront of light in medium $1$ having refractive index ${\mu }_1$ and $CD$ be the wavefront in medium $2$ having refractive index ${\mu }_2$. Choose the correct option.

• A. $\frac{\sin i}{\sin r}=\frac{{\mu }_2}{{\mu }_1}$
• B. $\frac{\cos i}{\cos r}=\frac{{\mu }_2}{{\mu }_1}$
• C. $\frac{\sin i}{\sin r}=\frac{{\mu }_1}{{\mu }_2}$
• D. $\frac{\cos i}{\cos r}=\frac{{\mu }_1}{{\mu }_2}$

Answer 1

The correct option is A $\frac{\sin i}{\sin r}=\frac{{\mu }_2}{{\mu }_1}$


Applying Huygens principle for refraction of light, we can show that

$\frac{\sin i}{\sin r}=\frac{v_{1}t}{v_{2}t}$

Where $v_1$ and $v_2$ are the speed of light in medium $1$ and $2$ respectively.

Since $\frac{v_1}{v_2}=\frac{{\mu }_2}{{\mu }_1}$

$\therefore \frac{\sin i}{\sin r}=\frac{{\mu }_2}{{\mu }_1}$

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