TIR needs both conditions
Total internal reflection (TIR): all light reflects back into the denser medium, none refracts across. It needs both conditions together: (1) light travelling from a denser to a less dense medium (e.g. glass → air); (2) angle of incidence (from the normal) greater than the critical angle . Below most light refracts out; at the refracted ray grazes the surface (refraction angle 90°); above , TIR. Naming only one condition scores half.
Critical angle: sin C = 1/n
For a denser medium (index ) meeting air, , so . It comes from Snell's law with refraction angle 90°: . A higher gives a smaller : glass ; dense glass ; diamond , so nearly all its light is trapped, giving the brilliance. TIR needs , not merely .
TIR uses: fibres, prisms, diamond
Optical fibres: the core has a higher than the cladding, so light striking the boundary above undergoes TIR and is guided along the fibre with little loss — used in telecommunications and endoscopes. 45° prisms (, ) turn light through 90° by TIR in periscopes and binoculars, brighter than absorbing mirrors. Diamond (, ) TIRs light many times for its sparkle.
Drawn from real examiner reports.
Only one TIR condition stated
The commonest incomplete TIR answer names just one condition. The mark scheme wants both: (1) denser → less dense medium, and (2) angle of incidence greater than the critical angle. "Angle exceeds " alone scores 1 of 2; "light hits at a steep angle" scores 0; the wrong direction scores 0. Also, "equal to " is not enough — TIR needs .
Writing C = 1/n instead of sin C = 1/n
June 2023 Paper 2P Q7 reported candidates "missed the sin" — writing instead of . For that gives , nonsense (real value ≈ 42°). Correct: . The same slip on gives . Always take sin, and check lands in 20°–70°.
June 2023 Paper 2P Q7(a)(ii)–(iv) — examiner report explicitly noted omission of sin from refractive-index formula as a common misconception; the same error directly affects sin C = 1/n questions.
TIR claimed from rare into dense medium
Some claim TIR happens going from a less dense to a denser medium (air → glass). Impossible: that direction always refracts, bending towards the normal, so light always transmits whatever the angle. TIR only occurs the other way (denser → less dense). Memory hook: dense-to-rare can be trapped; rare-to-dense always transmits.
Treating TIR as mirror reflection
TIR is not "light bouncing off a mirror". It happens inside the denser medium at the boundary — the light never leaves the glass, it reflects back in. Unlike a silvered mirror, which absorbs a little light, TIR reflects 100% with no loss. That is exactly why fibres and prisms use it instead of mirrors.
"Denser" mistaken for heavier
"Optically denser" means a higher refractive index, not physically heavier. Water () is optically denser than air; glass () is denser than water. TIR happens at the boundary the light is leaving — from higher into lower — so track the indices, not the weights.
Confusing i = C with i > C
Be precise about the critical angle itself. At exactly the refracted ray runs along the boundary (refraction angle 90°) and is not yet fully reflected; only for does true TIR occur, with no refracted ray. Below , the ray refracts out at less than 90°.
State both TIR conditions with an example
Asked to "state the conditions for TIR", write two bullets: (1) light travels from a denser to a less dense medium — name an example (glass → air); (2) the angle of incidence exceeds the critical angle. One bullet each = 2 marks; omit either and you cap at 1.
Calculator sequence for C = sin⁻¹(1/n)
For : compute , then press (INV SIN), with the calculator in degree mode. Sense-check the result lies between about 20° and 70° for typical IGCSE materials.
Find n from a critical angle
To find from a given critical angle, rearrange to — take the sine of the angle first, then divide into 1. Writing forgets the sine and gives , which is impossible for glass.
TIR ray diagram: reflected ray only
TIR ray diagram (for ): draw the boundary solid and the normal dashed; the incident ray inside the denser medium with marked at the normal; the reflected ray at back into the denser medium; no refracted ray. Label both media and the angles.
State the TWO conditions required for total internal reflection (TIR) to occur.
A glass block has refractive index . Calculate the critical angle for the glass-air boundary.
Give your answer to one decimal place.
