Revision summary

Match the equation to the pattern and its conditions. A standing-wave interval, an interference fringe and a diffraction minimum measure different things.

Superposition and standing patterns

In the linear model, add signed disturbances at the same position and instant. For vector quantities, add components. Coherent light requires electric-field addition before intensity is found; a pair of equal incoherent source images instead has intensities that add.

A standing wave can form from equal-amplitude, same-frequency waves travelling oppositely. Its nodes have zero amplitude at fixed positions. An instantaneous zero profile does not make every point a node. The ideal pattern has no net time-averaged energy transport along it.

For sound, a closed end is approximately a displacement node and pressure-variation antinode; an open end has the opposite conditions. A pressure node is not a vacuum. Successive closed/open resonant lengths differ by λ/2 when the effective-end correction is unchanged:

Revisit the stretched-string and microwave measurements for their distinct driver, reflector and detector roles, and the air-column experiment for length endpoints and end correction. Count intervals between matching positions, not the number of marked positions.

Coherence, phase and double slits

Coherent waves share a frequency and maintain a constant phase difference; they need not be in phase. Observable fringes also need overlap, sufficient stability and contrast, and compatible light polarisation components. Equal amplitude is needed for complete cancellation, rather than for every interference pattern.

Combine source phase with path difference. For in-phase sources, path differences nλ are constructive and (n + 1/2)λ are destructive. An initial antiphase relationship reverses those conditions. The water, sound and microwave demonstrations and light double-slit demonstration make the source and detector roles explicit.

Here a is slit separation, D the perpendicular screen distance and x the spacing between adjacent bright centres. The distant-screen, small-angle model gives path difference approximately ay/D at screen position y. Nine centres contain eight fringe intervals.

Distinguish maxima, minima and resolution

• Grating principal maxima: a sin θ = nλ for normal incidence. Convert line density to a spacing first. Require |nλ/a| ≤ 1, and count zero plus both signs of the allowed nonzero orders.
• Single-slit first minima: b sin θ = λ. With a small angle, the full central width is approximately 2λD/b, bounded by one first minimum on each side.
• Rayleigh criterion: θ_R ≈ λ/b in radians for the stated aperture-width model. Compare this limiting angle with the actual source separation.

For a grating screen measurement, y/D gives tan θ. Use the actual angle and its sine when the angle is not small. A wider aperture narrows its diffraction pattern and can improve resolution without moving the source centres.

a versus b: a separates neighbouring slits; b is the width of a single slit or aperture. x versus y: x is one fringe interval; y is a position from the central maximum. A grating equation locates maxima; a single-slit first-minimum equation locates minima.

Quantities and units

Symbols can be reused in different models: y is particle displacement in a string graph but screen position in optical geometry. Name the plotted quantity locally. A pressure amplitude is not measured in metres, and a normalised intensity profile does not provide an absolute power.

Read and measure the right feature

Keep source frequency, geometry, alignment and the relevant medium controlled. Locate corresponding nodes, minima, resonances or bright centres, and retain their original position readings with units. Use several intervals where appropriate and state the count.

Use a supplied calibrated scale rather than measuring a schematic drawing. Repeated readings assess variability; they do not fix parallax, an incorrect source model, changed detector orientation or an unaccounted end correction. For a grating, identify the order and zero direction before extracting the wavelength.