My name is Alexander FufaeV and here I write about:
Snell' Law of Refraction: How Light Rays Are Refracted in the Medium
Important Formula
$$n_1 \, \sin(\alpha_1) ~=~ \sin(\alpha_2) \, n_2 $$
$$n_1 ~=~ \frac{ \sin(\alpha_2) }{ \sin(\alpha_1) } \, n_2 $$
$$n_2 ~=~ \frac{ \sin(\alpha_1) }{ \sin(\alpha_2) } \, n_1$$
$$\alpha_1 ~=~ \arcsin\left( \frac{n_2}{n_1} \, \sin(\alpha_2) \right)$$
$$\alpha_2 ~=~ \arcsin\left( \frac{n_1}{n_2} \, \sin(\alpha_1) \right) $$
What do the formula symbols mean?
Refractive index of the 1st medium
$$ n_1 $$ Unit $$ - $$
Refractive index of one of the two media in which the light beam propagates. In vacuum, \( n_1 = 1 \).
Refractive index of the 2nd medium
$$ n_2 $$ Unit $$ - $$
Refractive index of the second medium into which the light beam is refracted.
Angle of incidence
$$ \alpha_1 $$ Unit $$ - $$
Angle of incidence from the incident beam in the first medium. Measured relative to the normal (a line perpendicular to the surface).
Angle of refraction
$$ \alpha_2 $$ Unit $$ - $$
Angle of refraction of the incident beam in the second medium. Measured relative to the normal.
Snell's law of refraction describes the behavior of light rays when passing from an optically denser medium into an optically less dense medium (or vice versa), such as from air into glass or from water into air.
If a ray of light enters a medium (e.g. water) with the refractive index \(n_1\) at the angle \(\alpha_1\) (between the perpendicular and the incident ray) from the medium (e.g. air), the angle of refraction \(\alpha_2\) (between the perpendicular and the incident ray) is determined by Snell' law of refraction:
$$ \begin{align} n_1 \, \sin(\alpha_1) ~=~ \sin(\alpha_2) \, n_2 \end{align} $$