Physics • Year 12 • Module 7 • Lesson 4
Diffraction and Diffraction Gratings
Lock in the key vocabulary, the grating equation, and the behaviour of single-slit and grating patterns before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. Write the matching term from this list in the right-hand column: diffraction, diffraction grating, grating element, order (n), central maximum, secondary maximum, single slit diffraction, resolving power, angular dispersion, minima. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The spreading of waves as they pass through an aperture or around an obstacle. | |
| 1.2 | An optical component with many thousands of closely spaced parallel slits that disperses light into component wavelengths. | |
| 1.3 | The distance d between adjacent slits in a diffraction grating; related to lines per metre by d = 1/N. | |
| 1.4 | An integer n = 0, 1, 2, 3, … that numbers successive maxima in a diffraction or grating pattern. | |
| 1.5 | The broad, bright central band in a single-slit diffraction pattern; twice as wide as the secondary maxima. | |
| 1.6 | Dimmer bands on either side of the central maximum in a single-slit pattern, where partial constructive interference occurs. | |
| 1.7 | The pattern produced when monochromatic light passes through one narrow opening, creating a wide central band flanked by dimmer side bands. | |
| 1.8 | The ability of an optical instrument or grating to separate two closely spaced wavelengths; increases with the number of illuminated slits. | |
| 1.9 | The rate of change of diffraction angle with wavelength; larger for finer gratings. | |
| 1.10 | Dark bands in a diffraction pattern where destructive interference causes zero intensity; positions given by a sin θ = nλ for a single slit. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 A narrower single slit produces a narrower diffraction pattern because less light passes through. T / F
2.2 The grating equation d sin θ = nλ applies to maxima (bright fringes) in a diffraction grating pattern. T / F
2.3 When white light passes through a diffraction grating, red light is deviated less than violet light because red has a shorter wavelength. T / F
2.4 The central maximum (n = 0) in a diffraction grating pattern is white when illuminated with white light. T / F
2.5 A grating with 1000 lines/mm has a larger grating element d than a grating with 500 lines/mm. T / F
2.6 Diffraction is evidence that light behaves as a wave, because particles would not spread out when passing through a slit. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
aperture · central maximum · grating element · interference · maxima · narrower · sharp · wavelength
Diffraction is the spreading of waves as they pass through an ___________. In a single-slit pattern, the ___________ is the widest and brightest region, flanked by progressively dimmer side bands. Making the slit ___________ causes the pattern to spread further, because θ is proportional to ___________ divided by slit width. A diffraction grating exploits ___________ from thousands of slits to produce very ___________ bright lines. The condition for these bright ___________ is d sin θ = nλ, where d is the ___________ (distance between adjacent slits).
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State what each symbol in the grating equation d sin θ = nλ represents and give its SI unit.
4.2 Explain why a diffraction grating produces sharper maxima than a double slit with the same slit spacing.
4.3 Describe what happens to the first-order maximum angle when the wavelength of light is increased.
4.4 Explain why there is a maximum order beyond which no bright maximum can be observed for a given grating and wavelength.
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “produces”, “determines”, “is evidence of”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: diffraction · wave nature of light · grating equation · grating element d · order n · angle θ.
6. Match the formula to its context
Four equations are listed in Column A. Match each to its correct description in Column B by writing the letter A–D. 4 marks (1 each)
| # | Column A — Equation | Column B — Description | Match |
|---|---|---|---|
| 6.1 | d sin θ = nλ | A. Position of minima in a single-slit pattern | |
| 6.2 | a sin θ = nλ | B. Grating equation giving angles of bright maxima | |
| 6.3 | d = 1/N | C. Fringe spacing on a screen for two slits | |
| 6.4 | Δx = λL/d | D. Grating element from lines per metre |
Q1 — Term–definition match
1.1 diffraction • 1.2 diffraction grating • 1.3 grating element • 1.4 order (n) • 1.5 central maximum • 1.6 secondary maximum • 1.7 single slit diffraction • 1.8 resolving power • 1.9 angular dispersion • 1.10 minima.
Marking notes. 1 mark per correct match. Accept minor wording variants (e.g. “grating spacing” for “grating element”).
Q2 — True / false with correction
2.1 False. A narrower slit produces a wider diffraction pattern. From a sin θ = nλ, smaller a gives larger θ, so the pattern spreads further (it is also dimmer because less light passes through).
2.2 True. The grating equation d sin θ = nλ gives the angles at which constructive interference (maxima) occur.
2.3 False. Red light has a longer wavelength than violet. Since sin θ = nλ/d, longer wavelength gives a larger angle, so red is deviated more than violet.
2.4 True. At n = 0, sin θ = 0 regardless of wavelength. All wavelengths of white light constructively interfere at the same point (the centre), producing a white central maximum.
2.5 False. A grating with 1000 lines/mm has a smaller grating element. d = 1/N, so more lines per unit length means smaller spacing between slits.
2.6 True. Diffraction (spreading through a slit) is a wave property. Classical particles travel in straight lines and would not spread; the observed spreading pattern is compelling evidence for the wave nature of light.
Q3 — Cloze paragraph
In order: aperture / central maximum / narrower / wavelength / interference / sharp / maxima / grating element.
Q4.1 — Grating equation symbols
d = grating element (m) — distance between adjacent slits. θ = angle of maximum from the central beam (degrees or radians — dimensionless). n = order number (dimensionless integer: 0, 1, 2, …). λ = wavelength of light (m).
Q4.2 — Why grating maxima are sharper than double slit
With many slits, constructive interference occurs only at the precise angles satisfying d sin θ = nλ. Slightly off those angles, the many sources destructively interfere with each other, producing very dark regions. A double slit has only two sources, so destructive interference is less complete, resulting in broader, less distinct maxima.
Q4.3 — Effect of increasing wavelength
From d sin θ = λ (first order, n = 1), increasing λ increases sin θ, so the first-order maximum moves to a larger angle (further from the centre). This is why red light (λ ≈ 700 nm) is diffracted at a greater angle than blue light (λ ≈ 450 nm).
Q4.4 — Why there is a maximum observable order
From d sin θ = nλ, sin θ cannot exceed 1. Therefore n ≤ d/λ. Any integer order greater than d/λ would require sin θ > 1, which is physically impossible. The maximum observable order is the largest integer n satisfying n ≤ d/λ.
Q5 — Sample concept map
Correct maps should include arrows such as:
- diffraction — is evidence of → wave nature of light
- grating equation — relates → grating element d
- grating element d — determines → angle θ
- order n — affects → angle θ
- grating equation — predicts → angle θ
- diffraction — is described by → grating equation
Award 1 mark per valid labelled arrow (minimum 6 marked).
Q6 — Formula matching
6.1 → B • 6.2 → A • 6.3 → D • 6.4 → C.
Note: Do not confuse Δx = λL/d (double-slit fringe spacing on screen at distance L) with the grating equation. The grating equation gives angles; the double-slit spacing formula gives a distance on a screen.