When is the refractive index above 1?

For any medium entered from vacuum or air, because light always travels slower in matter.

Where are the angles measured from?

Always from the normal, never from the surface; mixing them up spoils the whole item.

S4 Physics refraction paper 2: critical angle and total internal reflection

2026-11-10

Tutor Prep Guide · S4 Physics Refraction and Total Internal Reflection

Ten items start from sin C = 1 / n and cover water, glass, diamond, fibres and apparent depth.

Direct answers　Items 01 to 03 cover critical angles of three media, 04 to 06 fibres and apparent depth, 07 to 09 prisms and speed, and 10 writing n instead of 1 / n.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S4 Physics Refraction and Total Internal Reflection
Level	S4

02　Questions (10 items)

FoundationFind the critical angle for glass of n = 1.5.
FoundationWhat is the critical angle for water of n = 1.33?
FoundationDiamond has n = 2.42. Find its critical angle and explain the sparkle.
IntermediateA fibre has core n = 1.52 and cladding n = 1.48. Find the critical angle at the boundary.
IntermediateA pool is 2.0 m deep and n = 1.33. What is its apparent depth seen from above?
IntermediateA glass block looks 0.75 m thick and n = 1.5. Find its real thickness.
ChallengeLight enters one short face of a 45-45-90 glass prism (n = 1.5) normally. What happens at the hypotenuse?
ChallengeWhat is the speed of light in diamond of n = 2.42?
ChallengeLight in water (n = 1.33) meets air at 50 degrees. What happens?
Error redoA student writes sin C = n, gets 1.5 for glass and concludes there is no answer. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	41.8 degrees	sin C = 1 / n = 0.667, so C = 41.8 degrees; beyond it the ray is totally internally reflected.
2	48.8 degrees	sin C = 1 / 1.33 = 0.752, giving 48.8 degrees; water is less dense than glass so its critical angle is larger.
3	24.4 degrees	sin C = 1 / 2.42 = 0.413, so C = 24.4 degrees; a small critical angle traps light bouncing inside, which gives the sparkle.
4	76.8 degrees	Use the ratio: sin C = 1.48 / 1.52 = 0.974, so C = 76.8 degrees; the large angle keeps light in even on gentle bends.
5	1.5 m	Apparent depth = real depth / n = 2.0 / 1.33 = 1.5 m, so the pool looks shallower.
6	1.12 m	Real = apparent x n = 0.75 x 1.5 = 1.125 m, so reverse work multiplies.
7	Total internal reflection, turning the ray by 90 degrees	The incidence on the hypotenuse is 45 degrees, above the critical angle of 41.8 degrees, so the ray is totally reflected and the prism acts as a mirror.
8	about 1.24 x 10^8 m/s	v = c / n = 3.0 x 10^8 / 2.42 = 1.24 x 10^8 m/s, roughly forty per cent of the vacuum speed.
9	Total internal reflection, with no refracted ray	The critical angle is 48.8 degrees and 50 exceeds it, so all the light returns into the water with no refracted ray.
10	It should be sin C = 1 / n = 0.667, so C = 41.8 degrees	The formula is sin C = 1 / n, not n; a sine cannot exceed 1, so using n always fails.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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