The shape of the lesson
By the end of the lesson, learners can
- Measure the bending: Change the angle of incidence and read off the angle of refraction to see the refractive index that links them.
- One number, three meanings: The refractive index can be found from angles, from the critical angle, or from speeds.
- Trapping. Light hits the core boundary above the critical angle, so it is totally internally reflected and stays in the core.
- Drawing. The path is straight line segments meeting the boundary at sharp angles, never a curved or wavy line.
- Uses. Telecommunications (high capacity, low loss) and medical endoscopes.
One picture every idea returns to
The refractive index n equals sin(i) divided by sin(r), where i is the angle in air and r the angle in the medium. It also equals the speed of light in vacuum divided by its speed in the medium, and it links to the critical angle by n = 1 / sin(c). A larger n bends light more.
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, Counting the slowdown.. How much a material bends light can be captured in a single number. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Measure the bending | Change the angle of incidence and read off the angle of refraction to see the refractive index that links them. Project tab 3 of the lab (Refractive index) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: One number, three meanings | The refractive index can be found from angles, from the critical angle, or from speeds. Model the worked example Worked example on the board, one line at a time. | Connect-Extend-Challenge |
| 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 (6 questions, 16 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 One number, three meanings, 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.
Connect-Extend-Challenge
After the new idea, each student writes three lines: how it connects to what they knew, how it extends their thinking, and what still challenges them. Pairs compare, then the challenges become the plenary.
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 |
|---|---|
| In n = sin i / sin r, i is the angle in air (the less dense medium) and r the angle in the glass. | For the critical-angle relation n = 1 / sin c, the critical angle c is measured inside the denser medium. Mixing up which angle is which is the usual error. |
Refractive index: worksheet
6 questions, 16 marks. Written in the style of the papers; no past paper question is reproduced.
Define what is meant by the refractive index of a material, and write down the equation that links it to the angles of incidence and refraction.
A ray of light passes from air into a glass block. The angle of incidence is 50 degrees and the angle of refraction is 30 degrees. Calculate the refractive index of the glass.
A transparent plastic has a refractive index of 1.4. Calculate its critical angle.
Light travels at 3.0 × 10⁸ m/s in a vacuum and at 2.0 × 10⁸ m/s in a certain glass. Calculate the refractive index of the glass.
Two materials A and B have refractive indices of 1.33 and 1.52. (a) Which material bends light more? (b) Which has the smaller critical angle? Explain your answer to part (b).
A ray going from air into a glass block has an angle of incidence of 40 degrees and an angle of refraction of 25 degrees. (a) Calculate the refractive index. (b) State what happens to the frequency of the light as it enters the glass.
Answer key and marking notes
- The refractive index is a measure of how much the material slows down and bends light ✓
- n = sin i ÷ sin r, where i is the angle in air and r the angle in the material ✓
- n = sin i ÷ sin r = sin 50 ÷ sin 30 ✓
- = 0.766 ÷ 0.500 ✓
- n = 1.53, about 1.5 ✓
- sin c = 1 ÷ n = 1 ÷ 1.4 ✓
- sin c = 0.714 ✓
- c = 46 degrees (about 46 degrees) ✓
- n = speed in vacuum ÷ speed in the medium ✓
- n = (3.0 × 10⁸) ÷ (2.0 × 10⁸) = 1.5 ✓
- (a) Material B bends light more, because a higher refractive index means more bending ✓
- (b) Material B has the smaller critical angle ✓
- because sin c = 1 ÷ n, so a larger n gives a smaller critical angle ✓
- (a) n = sin 40 ÷ sin 25 = 0.643 ÷ 0.423 ✓
- n = 1.52, about 1.5 ✓
- (b) The frequency stays the same ✓
5 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.
A ray of light passes from air into glass. The angle of incidence is 50° and the angle of refraction is 30°. What is the refractive index of the glass?
- A0.65
- B1.5
- C1.7
- D2.0
Light travels from air into a glass block of refractive index 1.5 at an angle of incidence of 49°. What is the angle of refraction? (sin 49° = 0.75)
- A30°
- B33°
- C42°
- D73°
How is the refractive index of a material defined for light entering it from air?
- Asin(angle of incidence) ÷ sin(angle of refraction)
- Bangle of incidence ÷ angle of refraction
- Csin(angle of refraction) ÷ sin(angle of incidence)
- Dthe speed of light in the material × the angle of incidence
Light travels more slowly in material A (n = 1.5) than in material B (n = 1.3). Which statement is correct?
- AMaterial A is optically denser and refracts light more.
- BMaterial B is optically denser and refracts light more.
- CBoth materials refract light by the same amount.
- DNeither material refracts light.
As light passes from air into a denser, transparent medium, what happens to its wavelength and frequency?
- AThe wavelength decreases and the frequency stays the same.
- BBoth decrease.
- CThe wavelength increases and the frequency stays the same.
- DThe frequency decreases and the wavelength stays the same.
Quiz key
n = sin 50° ÷ sin 30° = 0.766 ÷ 0.500 = 1.5. Option A inverts the ratio (sin r ÷ sin i); the value must be greater than 1 for glass.
sin r = sin i ÷ n = 0.75 ÷ 1.5 = 0.50, so r = 30°. Option D multiplies instead of dividing, bending the ray the wrong way.
Refractive index n = sin i ÷ sin r, using the sines of the angles measured from the normal. Option B uses the angles directly, which is incorrect, and C inverts the ratio.
A higher refractive index means the light slows more and bends more, so material A (n = 1.5) is optically denser and refracts light more strongly than material B.
The frequency is unchanged on entering the medium, but the speed falls, so from v = fλ the wavelength decreases. The frequency does not change (ruling out B and D).
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.