Reflection · refraction · diffraction · interference
They are the same kind of thing obeying the same four rules, and the only difference is a number. Speech is about a metre long and a doorway is about a metre wide, so it fans out into the next room. Light is two million times shorter than that doorway, so it goes straight through and leaves a shadow with an edge.
This page covers reflection, refraction, diffraction and interference — the complete set of things any wave can do — and the ratio of wavelength to obstacle that decides which of them you notice. By the end you'll be able to:
Learn these four once and they never need learning again — they are identical for every kind of wave there is:
Searched as: reflection refraction diffraction interference, why does sound bend round corners, young double slit, constructive and destructive interference, ripple tank.
Predict the spreading angle, lock it, then close the gap towards the wavelength and watch the pattern open out. 🟢 real sinθ = λ/a engine
Guess, then lock — the bench waits until you commit.
Set a wavelength and a gap, then close the gap towards the wavelength and watch the pattern open out.
Four behaviours cover everything a wave can do. Six situations — name the behaviour before reaching for a formula.
An echo coming back across a canyon. What is the wave doing here?
Ask two things: is there more than one wave involved, and has anything changed its speed?
The same four apply to water, sound and light without a single change.
A 4 cm wave, and a target spreading angle. Choose the gap width that delivers it — 3 attempts.
Set the gap, then send the wave. sinθ = λ/a.
Each claim breaks something. Tap the broken idea.
The spreading angle is sinθ = λ/a, and amplitude appears nowhere in it. A whisper bends round the corner by exactly the same angle as a shout — it is simply quieter when it arrives.
The bend comes from one edge of a wavefront slowing before the other. Arrive square on and the whole front slows at once, so the speed changes but the direction does not — sin 0° is zero on both sides of Snell's law.
Cancellation at one place always comes with reinforcement at another. Add up the energy across the whole pattern and it matches exactly what the sources put in — interference moves energy about, it never removes it.
Thinking beats memorising. Sort every claim about waves into three boxes.
One wave, one opening, one decision. Everything here turns on a single ratio.
Divide the gap by the wavelength. That one ratio decides the whole answer.
Boats have to get in and the swell has to stay out, and those two wishes pull in opposite directions.
A narrow mouth lets less in, but fans out everything that does get in.
Read the scene. All three are one of the four behaviours wearing ordinary clothes.
Speech has a wavelength of roughly a metre and a doorway is roughly a metre wide, which is exactly the condition for dramatic diffraction. Light's wavelength is about two million times smaller than that opening, so it goes straight through and leaves a sharp-edged patch.
This is refraction, in water rather than glass. A wave slows as the water shallows, so the end of a crest that reaches shallow water first falls behind, and the whole line pivots until it is nearly parallel to the shore.
Part of the light reflects off the top of the film and part off the bottom, and the second has travelled slightly further. Where that extra path is a whole wavelength for a particular colour, that colour reinforces; where it is half, it cancels. The film's thickness varies, so the colours vary with it.
In plain terms: a wave is a pattern that travels, and there are only four things that can happen to it. Which one you notice depends almost entirely on how its wavelength compares with whatever it just met.
At a surface, part of a wave comes back and part goes on. The part that comes back leaves at the angle it arrived, which is i = r. The part that goes on changes speed, and if it arrived at an angle then one edge of each wavefront slows before the other, so the whole line pivots. That pivot is refraction, and it is caused by the change of speed rather than by the new material as such.
Past an edge or through a gap, a wave spreads. How much is given by sinθ = λ/a, and that formula contains only two lengths. A gap twenty wavelengths wide barely bends the wave; a gap one wavelength wide sends it out in every direction. Nothing about loudness, brightness or speed enters into it, which is the whole reason sound turns corners and light does not.
Where two waves overlap, the displacements add at every point. If crests arrive together the result is bigger; if a crest meets a trough they cancel. Whether that happens depends on the path difference: a whole number of wavelengths reinforces, a half-number cancels. This is why two slits give bands and why a soap bubble has colour, and it is the observation that proved light is a wave.
A wave entering a new material keeps its frequency and changes its speed and wavelength together, which is why colour does not change underwater. Past the critical angle nothing refracts out at all and you get total internal reflection, which is what keeps light inside an optical fibre. And where interference cancels, the energy has not gone: it has been moved to wherever the pattern is brighter.
Exams reward the method. Work it one step at a time — read the thought, predict the line, then reveal it.
Three small labs. The first two are the same formula read from opposite ends.
Six wrong ideas, most of them about which quantity is actually in the formula. Tap a card to bust the myth.
Every point on a wavefront acts as a new source of circular waves. The idea explained reflection and refraction at once, and it predicted diffraction long before anyone looked for it.
Light casts sharp shadows, which particles explain easily and waves apparently do not. Newton's authority held the question closed for a century.
Light through two narrow slits produced bright and dark bands. Particles cannot cancel each other; waves can, and do.
Poisson argued the wave theory absurdly predicted a bright point at the centre of a circular shadow. Arago looked, and it was there.
Light behaves as a wave in every experiment on this page and as a particle in the photoelectric effect. Newton and Huygens were each half right.
Narrow enough and the swell diffracts across the whole basin; wide enough and it passes straight through. Engineers have to pick a point between the two.
Long waves bend round terrain and short ones do not, which is why long-wave radio and line-of-sight television behave so differently.
Two reflections from a film thinner than a wavelength, adding and cancelling colour by colour as the thickness shifts.
One sentence each: which of the four is doing the work.
Drag the slider. Six wavelengths, and for each one, what it will and will not bend around.
Eleven orders of magnitude, four behaviours, and not one change to the rules.
Each one is a build and a measurement — the measuring is what turns a demo into a project.
Build: a shallow tray of water, a ruler tapped at one end, and blocks to make barriers and gaps.
Measure: photograph the pattern for three gap widths and measure the spreading angle on each photograph.
Build: a speaker behind a wall playing a low tone and then a high one at the same volume.
Measure: the loudness round the corner for several frequencies. The low notes reach much further.
Build: two fine slits cut in foil, a laser pointer, and a wall a couple of metres away.
Measure: the fringe spacing, then use w = λL/d in reverse to work out the laser's wavelength.
Build: a ripple tank with a submerged sheet of glass making one region shallower.
Measure: the angle of the wavefronts before and after the boundary, and check the ratio of the speeds.
Build: two speakers a metre apart playing the same steady tone in an open space.
Measure: walk a line in front of them and mark every quiet point. Compare the spacing with λL/d.
Build: a laser aimed at a CD's tracks, projecting spots onto a wall.
Measure: the angles of the spots, then work out the track spacing — and check it against the published 1.6 μm.
Straight answers, each one complete on its own:
Because diffraction depends on how the wavelength compares with the opening. Speech has a wavelength of about a metre and a doorway is about a metre wide, so the sound fans out into the next room. Visible light has a wavelength of around 500 nanometres, making that same doorway roughly two million wavelengths across, so the light goes essentially straight through and leaves a shadow with a sharp edge.
A change in the wave's speed. If a wavefront arrives at an angle, one end of it enters the slower material before the other end does, so that end falls behind and the whole line pivots. If the wave arrives square on, the speed still changes but every part of the front slows together, so nothing bends — which is exactly what Snell's law predicts when the angle is zero.
No. The frequency is set by whatever is generating the wave and stays the same throughout. What changes is the speed, and since v = fλ with f fixed, the wavelength must change by the same factor. This is why the colour you see does not change when you open your eyes underwater, even though the light is travelling more slowly there.
No. The spreading angle is given by sinθ = λ/a, which contains only the wavelength and the size of the opening. Amplitude — which is what loudness measures — appears nowhere in it. A whisper and a shout bend round the corner through exactly the same angle; the whisper is simply quieter by the time it gets to you.
It is redistributed rather than destroyed. Wherever an interference pattern has a dark or silent line, it has a correspondingly brighter or louder line elsewhere. Add the energy across the whole pattern and it comes to exactly what the sources put in. Interference rearranges energy in space; it never removes any.
Because the two waves must keep a fixed relationship in step — they must be coherent. Two separate lamps change phase randomly millions of times a second, so the bright and dark bands would shift far too fast to see and would average into uniform light. Splitting one source into two guarantees they stay locked together.
Refraction. Water waves travel more slowly where the water is shallower. If a crest approaches at an angle, the end nearest the shore reaches shallow water first and slows, while the far end is still moving quickly. The line pivots as a result, and by the time it breaks it is nearly parallel to the shoreline whatever direction it started from.
Diffraction. Light passing through the telescope's circular opening spreads slightly, so a point of light arrives as a small disc rather than a point. Two stars closer together than that disc blur into one. Since the spreading goes as λ divided by the aperture, the only fix is a bigger mirror — which is why large telescopes are built large.
Spot these before the exam does.
Seven question formats, the way LLOS.ai serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Four waves, one opening exactly a metre wide. Tap them in order, widest spread first. Then read the arithmetic — and look at the size of the gaps between them.
A long-wave broadcast signal, three hundred metres from crest to crest.
An ordinary spoken voice, about a metre from crest to crest.
A household wireless signal, twelve centimetres from crest to crest.
Red light, seven hundred nanometres from crest to crest.
Tap the four in the order you believe, widest spread through the gap first.
Four behaviours, one ratio, and no exceptions. A wave in a baking tray and a wave from a distant galaxy are doing exactly the same four things.