Superposition: Complete A Level H2 Physics Cheatsheet

Superposition and stationary waves

The principle of superposition: when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.

A stationary (standing) wave forms when two progressive waves of the same frequency and amplitude travel in opposite directions and superpose, usually a wave and its reflection. Points that never move are nodes, points of maximum oscillation are antinodes, and adjacent nodes are λ/2 apart. Energy is not transferred along a stationary wave.

You can use this to measure the wavelength of sound: set up a stationary wave (for example with a loudspeaker and a reflecting surface, or an air column), measure the distance between adjacent nodes, and double it.

Trap: Saying adjacent nodes are one wavelength apart. Node to node, or antinode to antinode, is half a wavelength. Node to the next antinode is a quarter.

Interference, coherence and the double slit

Interference is the superposition of waves from two or more sources. To see a stable interference pattern the sources must be coherent, with a constant phase difference, which means they also have the same frequency.

At a point where the path difference is a whole number of wavelengths (nλ), waves from coherent sources in phase arrive in phase and interfere constructively, giving a maximum. Where the path difference is (n + ½)λ they arrive in antiphase and interfere destructively, giving a minimum.

In Young's double-slit experiment, light from two narrow slits produces evenly spaced bright and dark fringes. The fringe separation is given by ax/D = λ, so x = λD/a. Fringes are clearer when the slits are narrow enough to diffract the light so the beams overlap, and the two sources have similar amplitudes.

Trick: For double-slit questions, rearrange to x = λD/a first. It shows instantly that fringes spread out with longer wavelength or a bigger screen distance, and squeeze together with wider slit separation.

Diffraction gratings, single slits and resolving power

Diffraction is the spreading of a wave as it passes through a gap or around an edge, most noticeable when the gap is similar in size to the wavelength.

A diffraction grating has many equally spaced slits. Sharp, bright principal maxima appear at angles given by a sin θ = nλ, where a is the line spacing. If a grating has N lines per metre, a = 1/N. Since sin θ can't exceed 1, the highest visible order is the largest whole number n ≤ a/λ. Measuring θ for a known a lets you determine the wavelength of light.

For a single slit of width b, the first minima on either side of the central maximum are at b sin θ = λ. The central maximum is twice as wide as the other maxima, and narrower slits give wider patterns.

Diffraction limits how well an aperture can separate two close sources. By the Rayleigh criterion, two sources are just resolved when the central maximum of one falls on the first minimum of the other, at an angular separation θ ≈ λ/b.

Trap: Forgetting to convert lines per mm into the spacing a in metres. 500 lines per mm means a = 1/(500 × 10³) = 2.0 × 10⁻⁶ m, not 1/500.

Worked Example

Light of wavelength 600 nm is shone normally onto a diffraction grating with 500 lines per mm.

Why this question is a good test of the topic: it uses the same symbol a for two different set-ups, so you have to know which equation applies, and part (b) tests the sin θ ≤ 1 limit rather than a straight substitution.

Frequently Asked Questions