The shape of the lesson
By the end of the lesson, learners can
- Push past the critical angle: Increase the angle of incidence inside the glass and watch the refracted ray vanish as the light is reflected back.
- Turning light with a prism: A right-angle glass prism turns light through 90 degrees by total internal reflection.
- Three stages of the angle: As the angle of incidence grows, the behaviour passes through three clear stages.
- Two conditions. Light must travel from the denser to the less dense medium, and the angle of incidence must be greater than the critical angle.
- Critical angle. The angle of incidence in the denser medium for which the angle of refraction is 90°.
- No leak. Past the critical angle there is no refracted ray. All of the light reflects.
One picture every idea returns to
When light travels from a denser to a less dense medium, increasing the angle of incidence reaches a critical angle at which the refracted ray runs along the surface. Beyond that angle, no light escapes: it is all reflected back, which is total internal reflection.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Trapped by the angle.. Past a certain steepness, light hitting the inside of a glass surface stops escaping altogether and bounces back as if the surface were a perfect mirror. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Push past the critical angle | Increase the angle of incidence inside the glass and watch the refracted ray vanish as the light is reflected back. Project tab 4 of the lab (Total internal reflection) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Turning light with a prism | A right-angle glass prism turns light through 90 degrees by total internal reflection. Project the simulation and let a student drive it while the class predicts. | Pairs |
| 21 to 30 min | Teach and check: Three stages of the angle | As the angle of incidence grows, the behaviour passes through three clear stages. | Frayer Model |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (7 questions, 17 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Three stages of the angle, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Frayer Model
Pairs fill a four-box grid for the key term: definition, characteristics, examples and non-examples. The non-examples box is where the misconceptions surface, so give it the most time.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Total internal reflection only happens when light travels from a denser to a less dense medium, such as glass to air, and only when the angle of incidence is greater than the critical angle. | Light going from air into glass can never be totally internally reflected. |
Total internal reflection: worksheet
7 questions, 17 marks. Written in the style of the papers; no past paper question is reproduced.
State the two conditions necessary for total internal reflection to occur.
Define the critical angle.
A ray of light inside a glass block travels toward the surface. Describe what happens to the light when the angle of incidence is:
(a) less than the critical angle, [1] (b) exactly equal to the critical angle, [1] (c) greater than the critical angle. [1]A student describes total internal reflection like this: "When the angle is bigger than the critical angle, most of the light reflects back but a faint refracted ray still escapes." Explain what is wrong with this statement.
The diagram shows a ray of light entering a right-angled glass prism and striking the sloping face from inside. The critical angle for the glass is 42°.
High-quality periscopes and binoculars use right-angled glass prisms rather than ordinary silvered mirrors to turn the light. Suggest two advantages of using prisms that rely on total internal reflection.
Diamond has a very small critical angle of about 24°, while window glass has a critical angle of about 42°.
(a) Explain what a smaller critical angle means for how easily light is totally internally reflected. [2] (b) Use this to suggest why a cut diamond sparkles much more than a similarly shaped piece of glass. [1]Answer key and marking notes
- The light must be travelling from a more dense to a less dense medium (toward the boundary from inside the denser one). ✓
- The angle of incidence must be greater than the critical angle. ✓
The critical angle is the angle of incidence, in the denser medium, for which the angle of refraction is 90°. ✓✓
"In the denser medium" and "refraction is 90°" are both needed for full marks.
(a) Most of the light refracts and escapes into the air, with a weak reflected ray inside. ✓
(b) The refracted ray travels along the surface (angle of refraction = 90°). ✓
(c) No light escapes. The light is totally internally reflected back into the glass. ✓
- There is no refracted ray at all once the angle of incidence exceeds the critical angle. ✓
- The reflection is total: 100 percent of the light is reflected back, so no faint ray escapes. ✓
(a) The angle of incidence at the sloping face is 45°, which is greater than the critical angle of 42°, and the light is inside the denser glass. Both conditions for TIR are satisfied. ✓✓
(b) Angle of reflection = 45° (equal to the angle of incidence). ✓
45° prisms are used in periscopes and binoculars precisely because 45° beats the critical angle of ordinary glass.
- Total internal reflection reflects 100 percent of the light, so the image is brighter than with a mirror, which absorbs some light. ✓
- There is no silvered coating to scratch, tarnish, or peel, so the prism stays effective and gives no faint double images. ✓
(a) A smaller critical angle means a larger range of incidence angles will exceed it, so light is totally internally reflected far more easily inside the diamond. ✓✓
(b) Light entering a diamond bounces around by TIR many times before leaving, so more light is sent back out toward the eye, giving the strong sparkle. ✓
Small critical angle, easy TIR, lots of internal bounces. That is the optics of a sparkle.
6 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
Which conditions are needed for total internal reflection to occur?
- ALight travels from a denser to a less dense medium, and the angle of incidence is greater than the critical angle.
- BLight travels from a less dense to a denser medium at any angle.
- CLight strikes the boundary along the normal.
- DThe two media have the same refractive index.
What is meant by the critical angle?
- AThe angle of incidence in the denser medium for which the angle of refraction is 90°.
- BThe angle at which light always reflects off a mirror.
- CThe angle of incidence equal to the angle of reflection.
- DThe smallest angle at which light can enter a glass block.
A transparent material has a refractive index of 1.5. What is its critical angle? Use sin c = 1 ÷ n.
- A34°
- B42°
- C48°
- D49°
The critical angle for a glass-to-air boundary is 42°. What is the refractive index of the glass? Use sin c = 1 ÷ n. (sin 42° = 0.67)
- A0.67
- B1.3
- C1.5
- D1.9
Light travelling inside glass strikes the glass-to-air boundary. Total internal reflection occurs only when the angle of incidence is:
- Agreater than the critical angle
- Bless than the critical angle
- Cexactly 0°
- Dexactly 90° to the normal
Light inside glass meets the boundary with air at an angle of incidence less than the critical angle. What happens?
- AMost of the light refracts out into the air, with a little weak reflection.
- BAll of the light is reflected back into the glass.
- CThe light is absorbed by the boundary.
- DThe light travels straight through without bending.
Quiz key
Total internal reflection needs light going from a denser to a less dense medium at an angle of incidence greater than the critical angle. Going into a denser medium (B) the light refracts out, it does not totally reflect.
The critical angle is the angle of incidence in the denser medium that gives an angle of refraction of 90°, so the refracted ray runs along the boundary. Beyond it, total internal reflection occurs.
sin c = 1 ÷ 1.5 = 0.667, so c = 42°. Option C (48°) comes from taking the inverse cosine instead of the inverse sine.
n = 1 ÷ sin 42° = 1 ÷ 0.67 = 1.5. Option A just quotes sin c; the refractive index must be greater than 1.
Total internal reflection happens only when the angle of incidence in the denser medium exceeds the critical angle. Below the critical angle (B) the light mostly refracts out into the air.
Below the critical angle the light refracts out of the glass into the air, although a small amount is partially reflected. Total reflection (B) only happens above the critical angle.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.