Refraction and total internal reflection
Snell's lawcritical angle formulaindex of refractionTIRBrewster's angle
Snell's law and the refractive index, with the critical angle, Brewster's angle and apparent depth that follow from bending light at a boundary.
Index of Refraction (n = c/v)
How much a medium slows light: the ratio of c to the speed of light in the medium.
Snell's Law of Refraction
Light bends at an interface so that n sin θ stays the same on both sides.
Critical Angle for Total Internal Reflection
Beyond this angle of incidence, light in the denser medium reflects totally instead of refracting.
Brewster's Angle
The incidence angle at which reflected light is completely polarized.
Apparent Depth
Viewed from straight above, an object under water appears at depth d/n.
How they fit together
Refractive index is just how much slower light goes in a material, n = c/v, and Snell's law is the geometric consequence at a boundary. Everything else on this page is a special case of Snell's law asked a different way. The critical angle is where the refracted ray would graze along the surface at exactly 90°; beyond it there is no refracted ray at all and the light reflects entirely — which is the whole basis of fibre optics and of the sparkle in a cut diamond, whose critical angle is a mere 24°.
Two conditions decide which formula you want. Total internal reflection only happens going from denser to less dense, so if n₁ < n₂ the critical angle does not exist and there is nothing to compute. Brewster's angle is a different question entirely — it is about polarisation, the angle at which reflected glare is fully polarised, which is why polarised sunglasses kill the shine off a wet road. Measure every angle from the normal, not from the surface; that single habit prevents most wrong answers here. Apparent depth is the everyday consequence: a pool looks about three-quarters of its real depth, and a stick in water looks bent.