Question

A beam of light propagating at an angle ${\alpha }_1$ from a medium $1$ through to another medium $2$ at an angle ${\alpha }_2$. If the wavelength of light in medium $1$ is ${\lambda }_1$, the wavelength of light in medium $2$, (${\lambda }_2$) is

• A. $\frac{\sin {\alpha }_1}{\sin {\alpha }_2}{\lambda }_1$
• B. $\frac{\sin {\alpha }_2}{\sin {\alpha }_1}{\lambda }_1$
• C. $\left(\frac{{\alpha }_1}{{\alpha }_2}\right){\lambda }_1$
• D. ${\lambda }_1$

Answer 1

The correct option is B $\frac{\sin {\alpha }_2}{\sin {\alpha }_1}{\lambda }_1$

Wavelength in a medium ${\lambda }_1=\frac{{\lambda }_0}{\mu }$
From Snell's law, $\frac{\sin {\alpha }_1}{\sin {\alpha }_2}=\frac{{\mu }_2}{{\mu }_1}=\frac{{\lambda }_1}{{\lambda }_2}$
$⟹$ ${\lambda }_2={\lambda }_1\frac{\sin {\alpha }_2}{\sin {\alpha }_1}$