When a wave crosses into a medium where its propagation speed changes, its direction can change. For light this bending is called refraction.

The refractive index of a medium is

$$n=\frac{c}{v},$$

where $v$ is the speed of light in that medium.

Snell's law

At an interface between media,

$$n_1\sin\theta_1=n_2\sin\theta_2,$$

where both angles are measured from the surface normal.

If light enters a medium with larger refractive index, it bends toward the normal. If it enters a smaller-index medium, it bends away from the normal.

Frequency and wavelength

The oscillation frequency remains continuous across the boundary, so the frequency does not change. Because

$$v=f\lambda,$$

the wavelength changes when the wave speed changes.

Partial reflection

Refraction does not imply that all the light enters the second medium. In general, part of the wave is reflected and part transmitted.

Snell's law describes the transmitted ray direction; the amount reflected and transmitted depends on the fields, polarization and material properties.