The Escape Angle
Critical angle — where refraction dies and reflection takes over
What this lesson covers
Why it matters
Shine a torch UP from underwater. Tilt it slowly… and at one exact angle the light stops leaving the water at all. The surface becomes a perfect mirror.
The idea in plain words
The escape condition. Tap each term.
sin C = 1 ÷ μ
Find the critical angle for diamond (μ = 2.42).
C ≈ 24.4° — tiny! Light entering a cut diamond can barely escape, so it bounces and sparkles
- degrees: C — critical angle — incidence (in the DENSER medium) for which r = 90°
- no unit: μ — refractive index of the denser medium
- the consequence: TIR — total internal reflection: beyond C, ALL light reflects — brighter than any mirror
- sin C = 1 ÷ 2.42 = 0.413
- C = sin⁻¹(0.413)
Predict first
Light inside glass (μ = 1.5) hits the surface at 50° from the normal. What happens?
For glass C = sin⁻¹(1/1.5) ≈ 41.8°. Beyond that, sin r would have to exceed 1 — impossible — so 100% of the light reflects: total internal reflection.
- It is totally reflected back inside — 50° is beyond the critical angle — correct
- It escapes, bending away from the normal
- It escapes along the surface
What you do
Sweep the underwater torch. Find the exact angle where the escaping ray dies — then find it again for a second medium.
Check yourself
Total internal reflection needs…
Both conditions matter: dense → rare AND beyond the critical angle. No silver involved — the surface itself does it, losslessly.
Exactly AT the critical angle, the refracted ray…
C is defined by r = 90° — the escaping ray grazes the surface before TIR takes over.
A mirage on a hot road is caused by…
Hot air near the tar is optically rarer; sky-light curving through it TIRs upward — you see the sky and read it as water.
- light going from denser to rarer, at i > C — correct
- light going from rarer to denser at any angle
- a silvered surface
- skims along the surface (r = 90°) — correct
- disappears
- goes straight up the normal
- gradual refraction + total internal reflection in layers of hot, rarer air — correct
- water actually condensing on the road
- sunlight reflecting off tar