Illustrated Physics
physics, drawn
How this site is made

The figure library

Every picture here is generated from code at build time. This page lists the generators, each rendered at its defaults.

No figure on this site is a drawing that was made once and saved. Each one is a function: it takes parameters and returns SVG, so the same generator produces the 27° incline and the 5° incline without either being redrawn.

That is the reason the collection can keep growing without the illustrations drifting apart. A generator is written once, checked once, and every essay that calls it inherits the same line weights, the same colour roles, and the same behaviour in dark mode. There are 30 of them so far.

beats

Beats between 10 and 11 cyclesTwo tones a little apart in frequency, added together. The rapid oscillation is the average frequency; the slow swelling is the difference, heard as a throb.00.511.52-202timebeat rate = 1 per unit timethe difference of the two frequencies

collision

An elastic collisionTwo bodies before and after a head-on collision. Momentum is the same on both rows by construction; kinetic energy is only preserved when the collision is elastic.before23.001-1.00momentum 5.00energy 9.50after20.3314.33momentum 5.00energy 9.50energy survives too — but only because e = 1

concave-mirror

A concave mirror forming a real imageAn object 2.50 focal lengths from a concave mirror. The image forms where the construction rays cross, inverted and magnified -0.67×.FCobjectimagethe mirror equation is the lens equation

critical-angle

The critical angle for n = 1.5 into n = 1Refracted angle against incident angle. It rises faster than the incident angle and reaches 90° at 41.8°, beyond which no refracted ray exists at all.020406080020406080incident angle (degrees)critical angle 41.8°beyond this, nothing emergesdashed: no bending at all

energy-exchange

Energy trading places through one swingKinetic and potential energy at successive moments of a swing. Each column has the same total height: whatever one loses the other gains.totalone end of the swingpassing the bottomthe other endkineticpotential

engine-efficiency

The ceiling on a heat engineMaximum possible efficiency against the ratio of cold to hot reservoir temperature. Reaching 100% would need a cold reservoir at absolute zero.00.20.40.60.8100.20.40.60.81cold ÷ hot temperature10%30%50%75%no engine, however clever, sits above this line

field-lines

The field of a dipoleField lines traced from a positive charge toward a negative one. Every line does eventually close on the negative charge, but the outer ones loop far outside any frame, so this picture is a crop rather than the whole field.+−

gaussian-surface

A closed surface with the charge insideEvery field line from the enclosed charge crosses the surface exactly once on its way out, so the net flux counts the charge.+every line leaves: net flux counts the chargethe shape of the surface never enters the answer

incline-free-body

A block on a 27° inclineFree-body diagram of a block resting on an inclined plane: weight straight down, resolved into a component pressing into the surface and one pulling along it, with friction opposing the slide.27°mgNmg sin θf

inverse-square

Why the field falls off as the squareThe same number of field lines crossing shells at one, two and three times the distance. The shell's area grows as the square of the radius, so the lines per unit area falls as its inverse.r = 1area × 1strength ÷ 1r = 2area × 4strength ÷ 4r = 3area × 9strength ÷ 9+nothing is lost between the shells —the same lines are simply more spread out

lens-equation

Image distance against object distanceImage distance in focal lengths against object distance in focal lengths. At exactly one focal length the image runs off to infinity; inside it the image distance goes negative, which means virtual.0.511.522.533.54-6-4-20246object distance (focal lengths)object at the focusvirtual imagesreal images

light-clock

A light clock at β = 0.6The same clock at rest and moving. Light covers the hypotenuse rather than the height, and since its speed is the same for both observers, the moving clock must take longer to tick.at restlight goes straight upmovinglight travels 1.25× as farγ = 1.250the ratio is forced by one constant speed

lorentz-factor

The Lorentz factor against speedHow much clocks slow and lengths shrink, plotted against speed as a fraction of light. At a tenth of light speed the effect is half a percent; it only becomes dramatic in the last stretch.00.20.40.60.80246speed (fraction of light)1.011.151.672.293.20everyday speeds live here, indistinguishable from 1

microstates

Ways to arrange 10 coinsThe number of distinct arrangements giving each number of heads, for 10 coins. Every individual arrangement is equally likely; the middle wins because there are more ways to reach it.1010145212032104252521061207458109110number of heads1,024 arrangements in total, all equally likelythe middle has 252 of them

pendulum

A pendulum displaced 32°A pendulum bob on a rod, with gravity resolved into a component along the rod and the restoring component perpendicular to it.θmgmg sin θ

pendulum-phase

The pendulum's phase portraitAngle plotted against angular velocity. Closed loops are swinging back and forth; the open curves above and below are rotating all the way round; the dashed curve between them is the separatrix.−π−π/2π/2π-22angleangular velocityat rest, hanging downbalanced upside downclosed: swingingopen: going over the topdashed: the boundary

projectile-angles

Trajectories at one speed and several anglesProjectile paths launched at the same speed and different angles. The 45° launch travels furthest; complementary angles land in the same place.00.20.40.60.8100.20.4range20°35°45°60°75°same speed, five angles45° goes furthest; 20° and 70° tie

pv-cycle

A Carnot cycle on pressure–volume axesTwo isothermal steps joined by two adiabatic ones, forming a closed loop. The area enclosed is the net work done by the gas over one cycle.123400.511.5volumepressure1234net workhot isothermcold isothermadiabatic steps

refraction

Refraction from n = 1 into n = 1.5A ray crossing a boundary between media of refractive index 1 and 1.5, bending by the amount Snell's law requires.40°25.4°n = 1n = 1.5some light always reflects as well

simultaneity

Simultaneity at β = 0.5Two events on the same horizontal line happen at the same time for the stationary observer. The moving observer slices spacetime along the tilted line, and for them one event happens before the other.xctsame time, for one observersame time, for the otherABneither slicing is the right one: that is the content of relativity

small-angle-error

The cost of assuming sin θ = θPercentage error in replacing sine of an angle by the angle itself, against the angle in degrees. Below about ten degrees it is under half a percent; by sixty it is over fifteen.02040608005101520amplitude (degrees)0.13%0.51%2.1%4.7%11.1%20.9%“small angle” is a claim about tolerance, not about physics

spacetime

A spacetime diagram at β = 0.5Position across, time up, in units where light travels at 45°. The shaded wedges are the future and past reachable by light; the tilted axes belong to an observer moving at 0.5 of the speed of light.xctlightct′x′here, nowfuturepastunreachableγ = 1.155 — the axes close on the light line together

speed-distribution

Molecular speeds at 4 temperaturesThe distribution of molecular speeds in a gas, with each curve enclosing the same area. Raising the temperature moves the peak right and lowers it: the same molecules, spread over a wider range of speeds.0123456700.20.40.60.8speedT = 0.5T = 1T = 2T = 4no molecule has the average speed; most are near it

standing-wave

Harmonics on a fixed stringThe first four standing-wave patterns on a string clamped at both ends. Only whole numbers of half-wavelengths fit, which is why the allowed frequencies are discrete.n = 1fundamentaln = 22× the frequencyn = 33× the frequencyn = 44× the frequency

superposition

Two waves 180° out of step, and their sumTwo sine waves differing in phase by 180 degrees, drawn faintly, with their sum drawn solid. The sum is computed point by point.00.511.52-2-1012positionphase difference 180°they cancel completely

thin-lens

A converging lens making a real imageAn object 2.44 focal lengths from a thin converging lens. The image sits where the construction rays cross, at 1.69 focal lengths, magnified -0.69×.FFobjectimageu = 2.44 fv = 1.69 fmagnification -0.69

travelling-wave

A travelling wave, caught at one instantA sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats; the ghosted curve is the same wave a moment later.00.511.522.5-101positionone wavelength

two-source-interference

Two sources 3 wavelengths apartCircular wavefronts from two sources, with the lines along which they arrive in step drawn through the pattern. Those lines are where the path difference is a whole number of wavelengths.sourcesourcesolid: waves arrive in stepbetween them they arrive opposed

vector-field

The same field, sampled as arrowsThe field at a grid of points, each arrow pointing the way a positive test charge would be pushed and scaled by the strength there.+−lines and arrows are the same fielddrawn two ways

velocity-components

Velocity along a trajectory, resolvedThe same arc with the velocity broken into components at several points. The horizontal part never changes; the vertical part falls steadily through zero at the top.00.20.40.60.8100.20.4horizontal: unchanged throughoutvertical: falls at a constant rate