Light bends at a boundary because its speed changes; going from a denser to a rarer medium beyond the critical angle, all of it is reflected back — total internal reflection.
How it's asked: Snell's law, apparent depth, critical angle from refractive index, conditions for TIR, and applications such as optical fibres, mirages and the sparkle of diamond.
Why this is true
Refractive index n = c/v measures how much light slows down in a medium. At a boundary the frequency cannot change (it is set by the source), so the wavelength shortens in the slower medium and the wavefront swings round, giving n₁ sin i = n₂ sin r. Going from a denser to a rarer medium the ray bends away from the normal, so as the angle of incidence grows the refracted ray approaches the surface. At the critical angle C the refracted ray grazes the surface (r = 90°), so sin C = n₂/n₁; beyond C no refracted ray is possible and all the light is reflected. Because nothing is lost to refraction, TIR is far more efficient than reflection from a mirror, which is why optical fibres can carry light over long distances.
Key points
Key formulae
Snell's law
n₁ sin i = n₂ sin r
Refractive index
n = c/v = λ(vacuum)/λ(medium)
Apparent depth
d' = d/n
Critical angle
sin C = n₂/n₁ = 1/n (into air)
Critical angles (into air)
| Medium | Refractive index | Critical angle |
|---|---|---|
| Water | ≈ 1.33 | ≈ 49° |
| Crown glass | ≈ 1.5 | ≈ 42° |
| Diamond | ≈ 2.42 | ≈ 24.4° |
Common traps
- TIR is impossible when light goes from a rarer into a denser medium, however large the angle.
- Frequency, not wavelength, stays the same when light enters a new medium — colour is set by frequency.
Worked example
A coin lies at the bottom of a tank filled with water (n = 4/3) to a depth of 12 cm. Viewed from directly above, how much does the coin appear to be raised?
High-yield
sin C = 1/n; TIR needs denser → rarer and i > C; frequency unchanged, λ shrinks to λ/n.
Quick check
Q1.The critical angle for light going from a medium of refractive index √2 into air is:
Q2.When light of wavelength 600 nm in air enters glass of refractive index 1.5: