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Refraction and total internal reflection

Light bends TOWARD the normal entering a denser medium, AWAY from the normal leaving one. Speed changes; frequency never does.

The two relationships worth knowing cold

Snell's law n₁ sinθ₁ = n₂ sinθ₂ θ measured from the normal, on each side of the boundary Refractive index and speed n = c / v(medium) A higher n means light travels SLOWER in that medium

What total internal reflection needs

  • Light travelling from a DENSER medium (higher n) toward a LESS dense one (lower n).
  • The angle of incidence GREATER than the critical angle for that boundary.
  • At exactly the critical angle, the refracted ray grazes along the boundary at 90°; beyond it, no light refracts out at all — it all reflects internally.
ℹ

What never changes at a boundary

FREQUENCY stays constant crossing any boundary — it is set by the source. Speed and wavelength both change together, in the same direction, so v = fλ still balances with f fixed. Worked example Speed of light in a medium from its refractive index A glass block has refractive index 1.52. Calculate the speed of light within the glass. v = c / n = (3.00 × 10⁸) / 1.52 v ≈ 1.97 × 10⁸ m s⁻¹ ✓ ≈ 1.97 × 10⁸ m s⁻¹ — always divide the speed of light in vacuum/air by the refractive index of the denser medium.

A fast check before applying total internal reflection

  • Have I confirmed light is travelling from a denser medium into a less dense one, not the reverse?
  • Have I compared the actual angle of incidence against the critical angle, rather than just asserting TIR occurs?

Practice for this standard covers the whole topic — flashcards and quiz.