Phase, coherence and superposition

What you will learn

Displacement, coherence, path and phase differences; interference applied to gratings.

Specification mapping: A1.3

Prerequisites: A1.1.2, A1.2

Physical principles

When waves overlap, the resultant displacement at a point is the algebraic sum of their separate displacements. This principle of superposition gives constructive interference when displacements reinforce and destructive interference when they oppose. Complete cancellation requires equal amplitudes and opposite phase.

Phase specifies position within an oscillation cycle. A whole cycle corresponds to 360° or 2π radians. A path difference Δx corresponds to phase difference 2πΔx/λ for waves of the same wavelength propagating in the same medium. Coherent sources maintain a constant phase difference and have the same frequency; equal brightness alone does not establish coherence.

A grating splits incident light into many coherent wave contributions from narrow, regularly spaced apertures. At particular angles, waves from adjacent apertures arrive in phase and reinforce sharply. For normally incident light, the supporting relation d sin θ = mλ describes constructive orders m. Here d is slit spacing, not total grating width. Treat this as an explanatory extension: the specification does not explicitly prescribe numerical use of the grating equation.

Scientific diagram and interpretation

Equations and relationships

Δφ = 2πΔx/λ; d sin θ = mλ (supporting extensions)

Worked examples and applications

Common misconceptions

Coherent does not mean permanently in phase; a fixed non-zero phase difference is coherent.

Examination technique

Connect path difference to phase, then explain reinforcement or cancellation.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.