DSE Physics | Waves and refraction lesson plan (for tutors) | From sin i and sin r to the critical angle

2026-11-03

Tutor lesson-prep guides · Secondary Physics

Students can quote n = sin i / sin r but start guessing when asked whether frequency changes on entering water. This lesson splits refraction into speed, wavelength and frequency, then moves on to the critical angle and optical fibres.

Objectives — Students can: (1) use n1 sin i = n2 sin r to get refraction angles 19.5, 28.1 and 35.3 degrees for i = 30, 45 and 60 degrees into glass; (2) explain that frequency is fixed while speed and wavelength both fall by 1/n, giving 2.0e+08 m/s and 400 nm inside glass; (3) compute the critical angle of glass to air, 41.8 degrees, and decide when total internal reflection happens; (4) use core and cladding refractive indices to explain why light stays inside a fibre.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Wave equation	How are speed, frequency and wavelength related?	v = f times lambda
Trigonometry	What is sin 30 degrees?	0.5
Everyday refraction	Does light bend towards or away from the normal entering water?	Towards the normal

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Opener	Why does a straw look broken in water? Draw the normal first	Normal and both angles correct
10-22 min	Snell law	n1 sin i = n2 sin r for three angles	19.5, 28.1, 35.3 degrees
22-34 min	Speed, wavelength, frequency	v = c/n = 2.0e+08 m/s, lambda = 600/1.5	400 nm, frequency fixed
34-46 min	Critical angle and TIR	sin c = n2/n1 = 1/1.5	c = 41.8 degrees
46-56 min	Fibres and applications	Core 1.52, cladding 1.48, c = 76.8	Explain the confinement
56-60 min	Exit check	Mark on the spot	Three correct

03 Teaching script (read it out)

Scene 1: Refraction is a change of speed, not a shortcut

Light travels at 3e+08 m/s in vacuum and 2.0e+08 m/s in glass, that is c/n. One side of the wavefront enters the slower medium first, so the wavefront turns: that is the whole mechanism. Keep three quantities apart. Frequency is set by the source and never changes at a boundary; speed and wavelength both shrink by 1/n, so 600 nm red light measures 400 nm in glass. Students often write that the colour changes; correct it by pointing out that colour follows frequency.

Ask them to: compute the ratio of the glass speed to c and say which two quantities share that ratio.

Scene 2: A critical angle only exists in one direction

Only dense to less dense has a critical angle: sin c = n2/n1 = 1/1.5, so c = 41.8 degrees. Below c you get partial reflection plus refraction; at c the refracted ray runs along the surface; above c everything reflects and no refracted ray exists. Going from less dense to more dense can never give total internal reflection because sin r stays below 1. Students often apply the critical angle to air into glass, which is always wrong.

Follow up: roughly what is the critical angle of water (n = 1.33) to air, and why is it larger?

Scene 3: An optical fibre is total internal reflection engineered

The core at 1.52 has a higher index than the cladding at 1.48, so any ray hitting the wall at more than 76.8 degrees reflects with almost no loss. The same idea explains periscopes, endoscopes and the sparkle of diamond, whose critical angle is about 24.4 degrees. In an exam answer give both the condition and the benefit: dense to less dense with the angle above the critical value, and a bendable path with no refracted leakage.

Ask them: why must the cladding index be lower than the core index?

04 Question types and worked steps

Type	Example	Steps	Answer
Calculation	Refraction angle from the angle of incidence	n1 sin i = n2 sin r, then inverse sine	i = 30 gives 19.5
Calculation	Refractive index from a critical angle	sin c = 1/n, so n = 1/sin c	c = 41.8 gives n = 1.5
Explanation	Which quantity is unchanged	Frequency is set by the source	Only frequency
Application	Fibres and total internal reflection	Compare indices, then angles	angle above 76.8

Sanity check (teach this): Check by substitution: sin r = sin 30 / 1.5 = 0.3333, so r = 19.47 degrees, matching a protractor reading. The other way, from glass to air at i = 41.8 degrees, sin r = 1.5 times sin 41.8 = 1.000, so r is exactly 90 degrees, which is the definition of the critical angle. Speed check: v = c/n = 3e+08/1.5 = 2.0e+08 m/s, and the wavelength scales by the same 1/1.5 while frequency stays at 5.0e+14 Hz.

05 Independent practice (3 questions)

Question	Answer	What to watch
Refraction angle for i = 45 into glass	28.1 degrees	sin r = sin 45 / 1.5
Critical angle of glass to air	41.8 degrees	sin c = 1/1.5
Wavelength of 600 nm light in glass	400 nm	600 / 1.5

06 Common mistakes and what to say

Mistake	Student writes	Say this
Saying frequency changes	“Light slows down so its frequency drops”	“Frequency is set by the source; speed and wavelength change, frequency does not.”
Looking for a critical angle from air	“Air into glass has a critical angle”	“Only dense to less dense has one, because sin r must reach 1.”
Measuring from the surface	Using the interface instead of the normal	“All angles are measured from the normal; draw it first.”
Giving the index a unit	Writing 1.5 m/s	“Refractive index is a ratio with no unit; speed carries the unit.”

07 Homework (paper, section and question numbers)

Physics chapter index — All chapters
Physics Paper 1 Section B — Questions 7-9: refraction and TIR

08 Exit check (last 5 minutes)

Question	Answer	Decision
Refraction angle for i = 30 into glass	19.5 degrees	Wrong: redo the sine step
Critical angle of glass to air	41.8 degrees	Wrong: return to script three
Which quantity never changes at a boundary	Frequency	Two or more wrong: reteach speed and wavelength

09 Tutor FAQ

Must students memorise indices?

Only air 1.00, water 1.33 and glass 1.50 are worth remembering.

Is the critical angle always under 45 degrees?

No: glass 41.8, water 48.8, diamond 24.4, all fixed by 1/n.

Is total internal reflection lossless?

Ideally there is no refracted leakage, but real fibres still absorb and scatter, so long links need repeaters.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.