How does Snell’s law calculate the angle of refraction?

In optics, Snell’s law describes the relationship between the path of a light ray crossing the boundary between two media and their respective refractive indices.12

To calculate the angle of refraction, the law is expressed by the following mathematical equation:

$$n_1\sin {\theta }_1=n_2\sin {\theta }_2$$

In this formula:
* $n_1$ and $n_2$ are the refractive indices of the first and second media, respectively.23
* ${\theta }_1$ is the angle of incidence, which is the angle between the incoming ray and the normal (a line perpendicular to the surface).13
* ${\theta }_2$ is the angle of refraction, measured between the refracted ray and the normal.13

By rearranging the equation to solve for the angle of refraction (${\theta }_2$), you get:

$${\theta }_2=\arcsin \left(\frac{n_1\sin {\theta }_1}{n_2}\right)$$

This relationship dictates that the light ray bends toward the normal when entering a medium with a higher refractive index and away from the normal when entering a medium with a lower refractive index.12