Illustrated Physics
physics, drawn
Concept

Focusing — where it appears

The concentration of a wave into a small region by giving its parts the phases that make them arrive in step there. The smallest spot travelling waves can make is about half a wavelength across, whatever the lens, mirror or recording that shapes them.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A reflection that keeps the angle to gravity and not to the wall. An internal wave beam of frequency 0.5N reflecting from a slope of 12°, with the wavelength ratio for slopes of 12°, 20°, 28° computed beside it. The frequency fixes the angle the energy makes with the horizontal — 30.0° here — because the restoring force is gravity and gravity is vertical, so the reflected beam must leave at that same angle whatever the wall is doing. Incident and reflected rays are therefore not mirror images, and the wavelength changes on reflection by sin(θ+α)/sin(θ−α). A flat floor gives one, checked exactly. A slope approaching the ray's own angle gives infinity, checked as the limit, and that is where a basin's internal tide is compressed until it breaks.

The reflection that changes the wavelength

An internal wave's frequency fixes the angle its energy makes with gravity, so a sloping wall cannot send it back the way a mirror would. The reflected beam leaves at the same angle to the vertical rather than the same angle to the wall, its wavelength changes by a factor that diverges when the slope matches the ray, and in a closed basin the changes accumulate until every ray in the fluid lies on one line.

fluids · Stratification The focus that gets sharper when the wave is scattered. The refocused amplitude against distance across the source, in wavelengths, for the same one-sided mirror and pulse, with the space between empty (dashed) and with a slab of 200 lossless point scatterers, 15 wavelengths thick, filling the space between source and mirror (solid). Through the slab the wave reaching the mirror is a jumble — scattered many times, arriving from every direction the slab can send it — yet time-reversed and sent back through the same slab, it refocuses on the source, in a spot 1.5 wavelengths wide against 4.8 in empty space. The scatterers, bouncing waves in from a wide range of angles, act as a lens much wider than the mirror: disorder that would ruin an ordinary lens makes a time-reversal mirror sharper.

The mirror that sends a wave back to where it began

Record a wave as it arrives at a row of microphones, then play each recording backwards through the loudspeaker beside it, and the sound converges on the place it came from — however twisted the route it took. Huygens said every point on a wavefront acts as a source; a time-reversal mirror takes him literally, making every point of a recorded front re-emit its own history in reverse. The result has a property no lens has. Put a thicket of scatterers between the source and the mirror, so that the arriving wave is an unrecognisable jumble, and the reversed wave still finds its way back — to a sharper focus than it could reach in empty space, because the disorder acts as a lens wider than the mirror.

waves · Huygens

Named alongside it

The objects these essays reach for when they reach for this one.

AnisotropyBoundary conditionBuoyancy frequencyDiffraction limitDispersion relationDissipationGroup velocityHuygens principleInternal wavesMixingMultiple scatteringPhase conjugation

All concepts