The shape of the lesson
By the end of the lesson, learners can
- Find the angles: Set the wavelength and the grating spacing and watch the orders appear at the angles given by d sinθ = nλ, with the highest visible order limited by sinθ ≤ 1.
- The grating equation: One relation handles every order.
- Reading the orders: The grating equation gives both the angles and a limit on how many orders exist.
- Equation: d sinθ = nλ.
- Spacing: d = 1/N.
- Limit: n ≤ d/λ.
One picture every idea returns to
A diffraction grating has many equally spaced slits. Maxima occur at angles given by d sinθ = nλ, where d is the slit spacing, θ the angle from the straight-through direction and n the order (0, 1, 2, ...). Because so many slits interfere, the maxima are much sharper and brighter than double-slit fringes, allowing a precise measurement of wavelength.
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, Thousands of slits, sharper maxima.. Replace two slits with thousands and the bright fringes become narrow, brilliant lines at precise angles. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Find the angles | Set the wavelength and the grating spacing and watch the orders appear at the angles given by d sinθ = nλ, with the highest visible order limited by sinθ ≤ 1. Project tab 4 of the lab (Diffraction grating) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: The grating equation | One relation handles every order. | Pairs |
| 21 to 30 min | Teach and check: Reading the orders | The grating equation gives both the angles and a limit on how many orders exist. | Corners |
| 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, 15 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 Reading the orders, 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.
Corners
Put one answer or viewpoint in each corner of the room. Students move to the corner they agree with, justify the choice to a partner there, then hear one voice from each corner before the reveal.
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 |
|---|---|
| Use sinθ, not tanθ or cosθ, in d sinθ = nλ. | The spacing d is the distance between adjacent slits, found from d = 1/N when N is the number of lines per metre, so more lines per millimetre means a smaller d and wider-spread orders. There is a maximum order, set by sinθ ≤ 1, so n cannot exceed d/λ. |
The diffraction grating: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
State the diffraction grating equation and define each symbol.
A diffraction grating has 500 lines per millimetre. Find the slit spacing d.
Light of wavelength 5.9 × 10⁻⁷ m falls on a grating with d = 2.0 × 10⁻⁶ m. Find the angle of the first-order maximum.
For the grating and light in question 3, find the highest order of maximum that can be observed.
Explain why a diffraction grating gives a more precise wavelength measurement than a double slit.
Light of wavelength 6.0 × 10⁻⁷ m falls on a grating with d = 2.5 × 10⁻⁶ m. Find the angle of the second-order maximum.
Answer key and marking notes
- d sinθ = nλ ✓
- d is the slit spacing, θ the angle of the maximum, n the order and λ the wavelength ✓
- d = 1 / N = (1 × 10⁻³ m) / 500 ✓
- d = 2.0 × 10⁻⁶ m ✓
- sinθ = nλ/d = (1 × 5.9 × 10⁻⁷) / (2.0 × 10⁻⁶) = 0.295 ✓
- θ = 17° ✓
- The maximum order has n ≤ d/λ = (2.0 × 10⁻⁶)/(5.9 × 10⁻⁷) = 3.4 ✓
- So the highest whole order is 3 ✓
- A grating has many slits, so the maxima are very sharp and bright ✓
- The angle of a sharp maximum can be measured accurately, giving a precise wavelength ✓
- sinθ = nλ/d = (2 × 6.0 × 10⁻⁷) / (2.5 × 10⁻⁶) = 0.48 ✓
- θ = 29° ✓
12 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.
The diffraction grating equation is:
- Ad sinθ = nλ
- Bd cosθ = nλ
- Cd tanθ = nλ
- Dd sinθ = λ/n
In the grating equation, d is the:
- Awidth of the pattern
- Border number
- Cspacing between adjacent slits
- Dwavelength
A grating has 400 lines per mm. Its slit spacing is:
- A400 m
- B2.5 × 10⁻⁶ m
- C4.0 × 10⁻³ m
- D2.5 × 10⁻³ m
Light of λ = 5.0 × 10⁻⁷ m on a grating with d = 2.5 × 10⁻⁶ m gives a first-order angle of:
- A0.20°
- B30°
- C5.7°
- D12°
In d sinθ = nλ, n is the:
- Aorder of the maximum
- Bnumber of lines
- Crefractive index
- Dfrequency
For λ = 5.0 × 10⁻⁷ m and d = 2.5 × 10⁻⁶ m, the highest order observable is:
- A2
- B4
- C5
- D50
Compared with a double slit, grating maxima are:
- Abroader and dimmer
- Bsharper and brighter
- Calways white
- Devenly spaced in distance
Using more lines per millimetre makes the orders:
- Acome closer together
- Bdisappear
- Cchange colour
- Dspread further apart
The zero-order maximum (n = 0) is:
- Astraight through, undeviated
- Bat 90°
- Cthe brightest colour split
- Dabsent
Light λ = 6.0 × 10⁻⁷ m, grating d = 1.67 × 10⁻⁶ m. The second-order angle is:
- A21°
- B36°
- C46°
- D90°
White light through a grating gives spectra because:
- Athe grating adds colour
- Bdifferent wavelengths diffract to different angles
- Cthe slits glow
- Donly red passes
A diffraction grating is used to measure wavelength because its maxima are:
- Abroad and easy to see
- Balways at 45°
- Cindependent of wavelength
- Dsharp, giving precise angles
Quiz key
d sinθ = nλ.
d is the slit spacing.
d = 1/N = (1 × 10⁻³)/400 = 2.5 × 10⁻⁶ m.
sinθ = λ/d = 0.20, θ = 12°.
n is the order (0, 1, 2, ...).
n ≤ d/λ = 5.0, so the highest order is 5.
Many slits make the maxima sharp and bright.
More lines means smaller d, so larger diffraction angles.
n = 0 gives sinθ = 0, straight through.
sinθ = 2λ/d = (1.2 × 10⁻⁶)/(1.67 × 10⁻⁶) = 0.72, θ = 46°.
d sinθ = nλ sends each wavelength to its own angle.
Sharp maxima allow precise angle and wavelength measurement.
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.