Solution

It is known that the refractive index determines the change in the speed of light in a medium compared to a vacuum. Therefore, by definition
$$c' = \frac{c}{n}$$
We also know that the energy of a photon is given by $E = h\nu$; this energy does not change when transitioning into another medium, so the frequency $\nu$ also does not change.

The wavelength is then defined as:
$$\lambda = \frac{c'}{\nu} = \frac{\lambda}{n}$$