Refraction

Refraction is the change a light ray's properties (speed, wavelength, direction of travel) undergo on crossing from one medium into another of different refractive index $n$. It is important to keep two related but distinct ideas separate: REFRACTION itself (the change in speed/wavelength on crossing the interface) happens every time light enters a new medium, whereas DEVIATION (an actual bending of the ray's path) happens only during OBLIQUE incidence -- at normal (perpendicular) incidence, refraction still occurs but there is zero deviation. (Deviation, as a general idea, applies to several other phenomena too, such as reflection, diffraction, scattering, and even the gravitational bending of light by a massive object.)

The ABSOLUTE REFRACTIVE INDEX of a medium is $n=\dfrac{c}{v}$, the ratio of light's speed in vacuum to its speed in that medium; as a ratio of two like quantities, it is dimensionless and unitless. Every material medium (air included) has $n>1$, since light travels fastest of all in vacuum. A medium of larger $n$ is called optically DENSER -- note carefully that this need not correspond to greater physical (mass) density: many oils, for instance, are optically denser than water while being physically less dense. The RELATIVE REFRACTIVE INDEX of medium 2 with respect to medium 1 is defined as $_1n_2 = \dfrac{n_2}{n_1} = \dfrac{v_1}{v_2}$, the ratio of the speed in medium 1 to the speed in medium 2.

A familiar illustration of refraction: viewed from outside, the bottom of a water body appears raised, because $n_{water} \approx \dfrac{\text{real depth}}{\text{apparent depth}}$. This relation holds equally well for a plane-parallel transparent slab: a point object O at real depth R, viewed from outside (air) through a slab of refractive index $n$, appears to be at a shallower apparent depth A. Using two paraxial rays from O -- one travelling straight up along the normal undeviated, one striking the surface obliquely and refracting -- and treating the angles of incidence $i$ and refraction $r$ as small (so $\tan\approx\sin$), one obtains $n=\dfrac{R}{A}=\dfrac{\sin i}{\sin r}$. …