An electromagnetic wave has a wavelength λ_0 in vacuum. It enters a...

When an electromagnetic wave travels from one medium to another, its frequency ($f$) remains constant.

The speed of the wave in vacuum is $c = f \lambda_0$, and in the medium it is $v = f \lambda$.

Therefore, the wavelength in the medium is directly proportional to the wave speed:
$\lambda = \lambda_0 \left(\dfrac{v}{c}\right)$

The speed of light in a medium is given by $v = \dfrac{c}{\sqrt{\mu_r \epsilon_r}}$.

Substituting this into the wavelength equation yields:
$\lambda = \lambda_0 \left( \dfrac{1}{\sqrt{\mu_r \epsilon_r}} \right) = \dfrac{\lambda_0}{\sqrt{\mu_r \epsilon_r}}$

Answer: $\dfrac{\lambda_0}{\sqrt{\mu_r \epsilon_r}}$