Refraction and apparent depth

Snell's law: sin i / sin r = n₂₁, the refractive index of medium 2 relative to medium 1; the incident ray, refracted ray and normal lie in one plane.

n₂₁ = n₂/n₁ = v₁/v₂: light slows down in the optically denser medium (larger n) and bends towards the normal on entering it.

The refractive index of a medium relative to vacuum is n = c/v, and n₁₂ = 1/n₂₁.

A ray passing through a parallel-sided slab emerges parallel to its original direction but shifted sideways (lateral shift); the shift grows with slab thickness and angle of incidence.

An object at the bottom of a water tank viewed from directly above appears raised: real depth / apparent depth = n of water relative to air.

For several layers stacked one on another, viewed nearly normally, the total apparent depth is the sum of each layer's thickness divided by its own refractive index.

The frequency of light does not change on refraction; its speed and wavelength change.