Refraction

definition:
The phenomenon where a beam of light changes direction when it travels from one medium to another.

Figure 1: Refraction at the interface of two media.
When light (such as a laser beam) enters another transparent isotropic medium, its propagation direction will change (see Figure 1). This phenomenon is called refraction. This is because at the boundary between two media, the incident light and transmitted light need to satisfy boundary conditions.
The tangential components of the wave vector are equal, otherwise the phase difference between the two waves at the boundary is related to their position, and the wavefront will be discontinuous. Due to the fact that the size of the wave vector is related to the refractive index of the medium, boundary conditions will only be satisfied in certain propagation directions. The exception is in the case of normal incidence, where the wave vector has no component at the interface.  
Based on the above discussion, Snell's law can be obtained:

  

Where n1 and n2 are the refractive indices of two media. It is obvious that media with lower refractive index correspond to a larger angle between the light beam and the normal.  
Figure 2 is a dynamic diagram of the refraction phenomenon. It can be seen that the wavelength in the medium on the right is shorter (due to slower light speed), and the refractive index of the medium on the right is higher. And the wavefront did not change at the interface, only the direction changed. This is due to a change in the transmission angle.  

Figure 2: Dynamic diagram of refraction phenomenon. The wavefront is represented by gray lines (only static images can be captured here). The change in wavefront direction comes from the decrease in the speed of light in the medium on the right side.  

Supplementary explanation
If the incident light comes from a medium with a high refractive index and a relatively large incident angle, not all exit angles satisfy Snell's law, because the maximum sine value of the exit angle is 1. In this case, it is impossible to obtain transmitted light and total reflection occurs.  
In non isotropic media, the refractive index is related to the polarization direction of light. Therefore, the refractive angle is also related to polarization.  
Refraction is often encountered in the fields of fundamental optics and photonics:

1. Refraction is commonly used in most optical lenses.  
2. When separating different wavelength components in a prism, it is necessary to use wavelength dependent refractive effects.  
3. By using birefringent materials, polarization dependent angles can also be obtained. This is used in some polarizers.  
4. Sometimes it is necessary to use optical forces related to beam displacement caused by refraction.  

Photon metamaterials with negative refractive index will produce unusual negative refractive effects. At this point, the refracted light and the incident light are located on the same side of the normal.