When Two Waves Meet: Interference in Action

How to use this simulation

1. Drag S₁ and S₂, or use the separation slider: a larger d packs the fringes closer together.
2. Switch the view to "time-averaged intensity" to replace the moving ripples with the fixed bright and dark fringes.
3. Put the probe P on a green line and the path difference is a whole number of wavelengths; on a red dashed line it is a half-integer.
4. Set the phase difference φ to 180°: every fringe shifts, and the centre line turns dark.

Two stones in a pond

Drop two stones into a still pond a short distance apart. Each one sends out rings of ripples, and soon the two sets of rings run through each other. Look closely and you will see a pattern: along some lines the water heaves up and down wildly, while along others it barely moves at all.

That pattern of loud and quiet places is interference. Where the two waves arrive in step they help each other; where they arrive out of step they cancel. The pattern is not random either. You can work out exactly where every calm line and every rough line will be before the stones even hit the water.

You carry an example of interference in your pocket if you own noise-cancelling headphones. They listen to the noise around you and play its mirror image into your ear, so the two sound waves cancel. Same physics, different wave.

Wave basics from scratch

A few words first. The highest point of a water wave is a crest and the lowest is a trough. The distance from one crest to the next is the wavelength, written λ (lambda). The biggest distance the water moves away from its resting level is the amplitude, A.

Phase describes where a particle is in its cycle at a given moment: at a crest, at a trough, rising or falling. Two points that rise and fall together are in phase. Two points where one is at a crest while the other is at a trough are completely out of phase, half a cycle apart.

Key words at a glance

These definitions come up again and again, so here they are in one place.

Conditions for constructive and destructive interference

What two waves do at a point depends on how they arrive there, and that depends on the path difference: how much farther one wave had to travel than the other.

Why the sources must be coherent

Shine two ordinary bulbs at a wall and you will never see fringes. Each bulb's light changes its phase randomly millions of times a second, so at any point the interference flips from constructive to destructive faster than any eye or camera can follow. All you see is the average.

A steady pattern needs coherent sources: the same frequency and a phase difference that stays fixed. The easy way to get them is to split one source in two, which is exactly what Young did with a pair of narrow slits.

• Same frequency (and so the same wavelength).
• Constant phase difference.
• Similar amplitudes, so the dark fringes are truly dark and the pattern is sharp.
• Narrow sources, close together.

Young's double-slit experiment, step by step

Around 1801 Thomas Young used a simple setup to show that light behaves as a wave. It is still the centrepiece of the topic in every physics syllabus.

Interference vs diffraction

Both produce bright and dark bands, which is why they get mixed up. The real difference is where the overlapping waves come from.

Experiments to try in the simulation

The ripple tank above is a small laboratory. Use it to check everything on this page for yourself.

• Increase the wavelength λ: the ripples lengthen and the green and red lines spread apart, just as β = λD/d predicts.
• Reduce the separation d: fewer lines, wider fringes.
• Sweep the phase difference φ from 0° to 360°: the whole pattern slides sideways and returns home at 360°.
• Lower the amplitude ratio: the dark fringes turn grey instead of black.
• Drag the probe P around and read the path difference in wavelengths from the readings panel.

Solved problems

Each problem is worked step by step. Convert everything to SI units first.

Common mistakes

Knowing these in advance saves marks.

• Mixing mm and nm in β = λD/d. Convert everything to metres first.
• Thinking energy is destroyed at dark fringes. It is only redistributed.
• Thinking a larger d gives wider fringes. It is the reverse.
• Expecting two separate bulbs to interfere. They are not coherent.
• Confusing interference with diffraction. Ask: two sources, or one wavefront?

Interference in everyday life

Interference is not just a textbook experiment. It is happening around you all the time.

• Soap bubbles and oil films: light reflected from the front and back surfaces of a thin film interferes. Different thicknesses reinforce different colours, which is where the rainbow swirls come from.
• Anti-reflection coatings on glasses and camera lenses: a very thin layer makes the reflections from its two surfaces cancel, so less light bounces off and more gets through.
• Noise-cancelling headphones: a microphone picks up outside noise and the headphones play the same sound 180° out of phase. The two interfere destructively, which works best on steady sounds like engine hum.
• Radio and Wi-Fi dead spots: signals reflected off walls interfere with the direct signal, so a few spots in a room get a weaker connection.

Exam corner

These question types come up most often.

• Define coherent sources and explain why two separate lamps cannot produce a steady interference pattern.
• State the conditions for constructive and destructive interference in terms of path difference and phase difference.
• Calculate the fringe width for given λ, D and d. With this page's numbers, β = 1.2 mm.
• Explain how the pattern changes when d is halved, the screen is moved back or the apparatus is placed in water.
• Distinguish between interference and diffraction.

Quick revision

Read this the night before a test and the main ideas will come back.

• Superposition: y = y₁ + y₂.
• Interference needs coherent sources.
• Constructive: Δ = nλ, amplitude A₁ + A₂.
• Destructive: Δ = (2n + 1)λ/2, amplitude |A₁ − A₂|.
• Phase difference δ = (2π/λ)Δ.
• Fringe width β = λD/d.
• Energy is redistributed, never destroyed.

Frequently asked questions