Question

A red colour light of wavelength $760\text{nm}$ is observed to pass from air to an unknown medium. If the wavelength of light in unknown medium becomes $570\text{nm}$, the unknown medium is

Answer 1

Refractive index, $\mu =\frac{{\lambda }_{\text{vaccum}}}{{\lambda }_{\text{medium}}}$
$\Rightarrow \mu \propto \frac{1}{\lambda }$
$\because {\lambda }_1=760\text{nm},{\lambda }_2=570\text{nm}$
$\Rightarrow {\lambda }_1>{\lambda }_2$
or, ${\mu }_2>{\mu }_1$
Thus, unknown medium is optical denser.

Tips: Relate Snell's law with the wave properties $(v,\lambda )$ of light.