What evidence shows that light behaves as a wave, and how do waves combine when they overlap?
Describe the wave model of light and apply the principle of superposition to constructive and destructive interference.
The wave model of light, the principle of superposition, and how path difference determines constructive and destructive interference, with worked examples.
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What this dot point is asking
You need to describe the wave model of light and apply the principle of superposition to predict where constructive and destructive interference occur.
The wave model
In the wave model, light is a wave with the usual wave properties:
where is the wave speed (for light in a vacuum, ), the frequency (Hz) and the wavelength (m). Visible light has wavelengths from roughly 400 nm (violet) to 700 nm (red).
The wave model successfully explains reflection, refraction, diffraction (bending around obstacles and through gaps) and, crucially, interference - none of which a simple particle model handles. Interference is the strongest classical evidence that light is a wave.
The principle of superposition
Superposition leads to two extreme outcomes:
- Constructive interference: crests meet crests (and troughs meet troughs). The waves are in phase and reinforce, giving a larger amplitude - a bright fringe for light.
- Destructive interference: a crest meets a trough. The waves are out of phase and cancel, giving zero (or reduced) amplitude - a dark fringe.
Path difference decides the outcome
For two waves from sources in phase (same frequency and starting phase), what matters is the difference in the distances they travel to reach a point - the path difference.
For this stable pattern to be visible, the two sources must be coherent - they keep a constant phase relationship (same frequency and a fixed phase difference), as from a single source split into two.
Exam-style practice questions
Practice questions written in the style of SACE Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
2024 SACE Stage 23 marksTwo vertically oriented transmitting antennas A and B produce electromagnetic waves with a wavelength of 62.5 m. A receiving antenna at point P is 30.0 km from antenna A and 40.0 km from antenna B. Determine whether the electromagnetic waves received at point P are at maximum or minimum amplitude.Show worked answer →
Whether the waves interfere constructively (maximum) or destructively (minimum) depends on the path difference compared with the wavelength.
Path difference = 40.0 km - 30.0 km = 10.0 km = 10 000 m.
Divide by the wavelength: 10 000 / 62.5 = 160. This is a whole number of wavelengths.
A path difference equal to a whole number of wavelengths (160 in this case) means the waves arrive in phase, so they interfere constructively. The waves at point P are at maximum amplitude.
1 mark for the path difference, 1 mark for dividing by the wavelength to get a whole number, 1 mark for concluding maximum amplitude (constructive interference).
2023 SACE Stage 23 marksIn a two-slit experiment using a sodium vapour lamp, a pattern of dark and light fringes was observed on a screen. Explain the production of the dark fringes observed on the screen.Show worked answer →
Light from the two slits spreads out and overlaps on the screen. Because the light is coherent, the two sets of waves can be combined using the principle of superposition.
A dark fringe forms where the two waves arrive exactly out of phase, so that a crest from one slit meets a trough from the other. This is destructive interference, and the waves cancel to give zero (minimum) amplitude.
This happens at positions where the path difference between the two slits is an odd number of half wavelengths (half a wavelength, one and a half wavelengths, and so on).
1 mark for superposition of waves from the two slits, 1 mark for destructive interference (crest meets trough), 1 mark for stating the path difference is an odd number of half wavelengths.