The questions are on the wave interference test. Take it under real conditions before reading the mark scheme.
Quick answer: Superposition means waves add their displacements where they meet. This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on wave interference, from path difference to grating versus two slits, with the equivalent answers to accept.
Model answers with a marking guide. Award method marks for correct rearrangement and substitution even if the final value is wrong, and check units and powers of ten.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB C.3
Question 1 Path difference (3 marks)
- 1.65 × 10⁻⁶ ÷ 550 × 10⁻⁹ = 3 λ.
- A whole number of wavelengths, so constructive.
- Same frequency and a constant phase difference.
Marking: 1 mark for each part.
Question 2 Young double slit (3 marks)
- w = λD/s = 480 × 10⁻⁹ × 1.80 ÷ 0.20 × 10⁻³ = 4.32 mm.
- The spacing halves.
Marking: (a) 1 for substitution, 1 for answer with unit; (b) 1.
Question 3 Grating at work (3 marks)
- d = 4.00 µm. sin θ = 600 × 10⁻⁹ ÷ 4.00 × 10⁻⁶ = 0.15, θ = 8.63°.
- d/λ = 6.67, so the highest order is 6.
Marking: (a) 1 for sin θ, 1 for angle; (b) 1.
Question 4 Reading a pattern (3 marks)
- 3.0 mm.
- λ = ws/D = 3.0 × 10⁻³ × 0.40 × 10⁻³ ÷ 2.0 = 0.000 m = 600 nm.
Marking: (a) 1; (b) 1 for rearrangement/substitution, 1 for answer.
Question 5 Two torches (2 marks)
Atoms in a torch emit light in random bursts, so the phase difference between two torches changes constantly and no fixed bright or dark positions form. A laser beam divided by the two slits gives two sources derived from the same wave, so their phase difference stays constant and a stable pattern forms.
Marking: 1 for random phase from separate sources; 1 for constant phase difference from the same wavefront.
Question 6 White light fringes (2 marks)
The central fringe is white because every wavelength has zero path difference there. Other fringes are coloured spectra because w = λD/s differs for each colour; violet (shortest λ) is nearest the centre and red is furthest.
Marking: 1 for white centre with reason; 1 for coloured fringes with violet inside and red outside.
Question 7 Fringes in water (2 marks)
In water the wavelength is λ ÷ 1.33, so w also falls by 1.33: w = 4.0 ÷ 1.33 = 3.01 mm.
Marking: 1 for wavelength reduced by n; 1 for the new value.
Question 8 Grating versus two slits (2 marks)
Many slits all contribute, so the waves are in step only at the exact grating angles. At other angles the large number of waves with different phases cancel almost exactly. More light is also transmitted in total, so the maxima are narrow and bright.
Marking: 1 for cancellation almost everywhere; 1 for narrow and bright maxima.
