Q.Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is 1.5 and the frequency of light is $3.5\times10^{14}$ Hz, find the wave number of light in glass. [Velocity of light in air $c=3\times10^{8}$ m/s]

Frequency stays the same on refraction; wavelength shrinks by a factor of $\mu$, so use $\lambda_{air}=c/f$ and $\lambda_{glass}=\lambda_{air}/\mu$.

When light passes from one medium to another, its frequency remains unchanged (it is fixed by the source), but its speed and wavelength change (the wavelength is what physically shortens inside the denser medium).

Wavelength in air:

$\lambda_{air}=\frac{c}{f}=\frac{3\times10^{8}}{3.5\times10^{14}}\approx 8.571\times10^{-7}\text{ m}$

Wavelength in glass ($\mu=1.5$):

$\lambda_{glass}=\frac{\lambda_{air}}{\mu}=\frac{8.571\times10^{-7}}{1.5}\approx 5.714\times10^{-7}\text{ m}$

Change in wavelength (decrease):

$\Delta\lambda=\lambda_{air}-\lambda_{glass}\approx 8.571\times10^{-7}-5.714\times10^{-7}=2.857\times10^{-7}\text{ m}$

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