The phenomenon of refraction had been observed for centuries, but it was not until 1621 that its cause was stated mathematically.
Willebrord Snell (1591–1626) was a Dutch astronomer and mathematician who is credited with identifying the exact relationship between the angle of incidence and the angle of refraction.
Snell’s law is a formula that uses values for the index of refraction to calculate the new angle that a ray will take as a beam of light strikes the interface between two media.
If you call the indices of refraction of the two media n 1 and n 2 and call the angles of incidence and the angle of refraction θ 1 and θ 2, then the formula for Snell’s law is: n 1 sinθ 1 = n 2 sinθ 2
Sometimes, such as in the case of fibre optics, light does not pass from one medium to another but stays within the medium.
In total internal reflection, light reflects completely off the inside wall of a denser medium (higher index of refraction) rather than passing through the wall into a less dense medium (lower index of refraction).
Recall that when light passes from a denser material, such as water, into a less dense medium, such as air, the light refracts away from the normal.
As the angle of incidence increases, the angle of refraction increases. At a certain angle, called the critical angle, the refracted ray of light follows a path exactly along the surface of the water. Even though the light refracts, it does not leave the water. In a way, the light is “trapped” inside the water
When light crosses a boundary between materials with different indices, the light beam will be partially refracted at the boundary surface, and partially reflected.