Waves and superposition: models, interference and diffraction
Key idea: Use signed displacement and phase consistently across time and space, then apply superposition to standing waves, interference and diffraction without confusing their distinct conditions.
Before you start: Oscillations objective chainQuantities & Measurement objective chain
By the end, you can
- Model mechanical and electromagnetic progressive waves, interpret time and position graphs, and use wave quantities, phase and energy transfer.
- Apply intensity–amplitude and inverse-square relationships, and use polarisation and Malus' law for electromagnetic waves.
- Apply superposition and explain standing-wave experiments, boundary conditions, nodes, antinodes and sound-wavelength measurement.
- Analyse coherent two-source interference and Young double-slit fringes using phase and path difference.
- Use diffraction gratings, single-slit first minima and the Rayleigh criterion with their distinct aperture spacings and assumptions.
Starting-point self-check
1. Check your starting point
Attempt all seven groups without notes and mark the first graph axis, phase conversion, boundary condition or aperture spacing you could not justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Two-source interference and Young double slit 11(e)–(h)
Question 1
Light of wavelength 600 nm passes through slits 0.300 mm apart onto a screen 2.00 m away. Find fringe spacing and state the source and overlap conditions needed for stable visible fringes.
Check the model response
x = λD/a = (600 × 10⁻⁹)(2.00)/(0.300 × 10⁻³) = 4.00 mm. The sources must be coherent: same frequency with constant phase difference. Their waves must overlap, have compatible polarisation and sufficiently similar amplitudes for useful contrast.
repair
2. Repair the eleven common breaks
Use only the repair matching an error, then redraw the axes, signed displacement, boundary conditions, rays or aperture before retrying.
Two-source interference and Young double slit 11(e)–(h)
Check this idea
Misconception: Same frequency alone guarantees stable interference fringes.
Repair: The sources must maintain a constant phase difference, and the waves must overlap with compatible polarisation and useful amplitude contrast.
worked example
3. Follow seven worked models
Follow how each solution fixes the graph type, energy-spreading model, transmission axis, boundary condition, path difference or aperture before calculating.
Two-source interference and Young double slit 11(e)–(h)
Model 1
Two coherent water waves of wavelength 0.120 m reach a point with path difference 0.300 m. Find phase difference and classify the interference.
Check the model response
Path difference is 0.300/0.120 = 2.5 wavelengths, so Δφ = 2π(2.5) = 5π rad, equivalent to π rad. The waves arrive in antiphase and interfere destructively if their amplitudes are equal.
guided practice
4. Guided practice
Use each hint only to select the graph interval, spreading surface, polarisation reference, mode shape, interference condition or aperture equation.
Two-source interference and Young double slit 11(e)–(h)
Question 1
Two coherent sources have wavelength 0.50 m. At P their path difference is 1.25 m. Find phase difference and classify P.
Hint: Convert path difference to wavelengths before deciding integer or half-integer.
Check the model response
1.25/0.50 = 2.5 wavelengths, so Δφ = 5π rad, equivalent to π. P is a destructive minimum for equal amplitudes.
independent practice
5. Independent practice
Solve without repair notes and state the graph, source, boundary, coherence and aperture assumptions used.
Two-source interference and Young double slit 11(e)–(h)
Question 1
Derive x = λD/a for adjacent Young double-slit fringes using small-angle geometry and state two visibility conditions beyond the path-difference rule.
Check the model response
For a point at transverse distance y, path difference ≈ a sinθ ≈ ay/D. Adjacent maxima differ by one λ, so aΔy/D = λ and x = λD/a. Sources must be coherent, and waves must overlap with compatible polarisation and sufficiently similar amplitudes.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Two-source interference and Young double slit 11(e)–(h)
Question 1
Define coherence and path difference. For λ = 480 nm, slit separation 0.20 mm and screen distance 1.50 m, find Young fringe spacing and list the conditions for observable fringes.
Check the model response
Coherent sources have the same frequency and constant phase difference. Path difference is the difference in distances travelled to a point. x = λD/a = (480 × 10⁻⁹)(1.50)/(0.20 × 10⁻³) = 3.60 mm. Waves must overlap, remain coherent, have compatible polarisation and useful amplitude contrast.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Two-source interference and Young double slit 11(e)–(h)
Question 1
At a point, coherent waves of wavelength 0.36 m have path difference 0.81 m. Find phase difference and decide whether the point is a maximum, minimum or neither.
Check the model response
Path difference is 0.81/0.36 = 2.25 wavelengths, so Δφ = 4.5π rad, equivalent to π/2. It is neither a maximum nor a minimum for equal in-phase sources.