Superposition Notes

What these notes cover

These notes cover superposition for Cambridge International AS Level Physics (9702): the principle of superposition, constructive and destructive interference, path difference and phase difference, the conditions needed for an observable interference pattern including coherence, two-source interference and the double-slit experiment, diffraction and the diffraction grating. They include worked examples and many past-paper questions with solutions.

Key formulas and definitions

• Principle of superposition: when two or more waves meet at a point, the resultant displacement is the sum of the individual displacements.
• Constructive interference occurs where waves meet in phase: path difference = nλ (0, λ, 2λ, …), phase difference = 0, 360°, 720°, …
• Destructive interference occurs where waves meet in antiphase: path difference = (n + ½)λ (λ/2, 3λ/2, …), phase difference = 180°, 540°, … With equal amplitudes the resultant amplitude is zero.
• To see a stable interference pattern, the sources must be coherent: they have a constant phase difference, which needs the same frequency (and wavelength).
• Double-slit interference: λ = ax / D, where a is the slit separation, x the fringe separation and D the distance from the slits to the screen.
• Diffraction is the spreading of a wave as it passes through a gap or around an edge. It is most noticeable when the gap is similar in size to the wavelength.
• Diffraction grating: d sin θ = nλ, where d is the spacing between adjacent lines and n is the order of the maximum.
• Phase difference = (path difference ÷ λ) × 360°. The wave equation v = fλ links speed, frequency and wavelength.