Illustrated Physics
physics, drawn
Depth

Series — page 3

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
Rays through a raindrop. Parallel rays entering a spherical drop at different heights, refracting in, reflecting once from the back, and refracting out. The outgoing rays crowd together near one particular direction, and that crowding is the bow.

Dispersion

  1. 1 The angle the rainbow has to be, and why nobody chose it
  2. 2 Two glasses that cancel a derivative
  3. 3 The wavelength a fibre does not smear
  4. 4 The ring at twenty-two degrees
  5. 5 The delay that is a random variable
  6. +4 more
9 essays · optics A harmonic well. Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.

Energy

  1. 1 The hill that gives it back, and the forces that do not
  2. 2 The energy that depends on the observer
  3. 3 The speed at which grip hands over to power
  4. 4 The floor that does no work
  5. 5 The wall that moves while the ball is in flight
  6. +4 more
9 essays · mechanics A block on a 27° incline. Free-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.

Free-body

  1. 1 The slope, and the two directions that make it easy
  2. 2 Slide or topple
  3. 3 The table statics cannot settle
  4. 4 The load nobody applied
  5. 5 A state no load could reach
  6. +4 more
9 essays · mechanics What friction returns, against what it is asked for. The friction force on a block under a 50 N normal load, against the force applied to it. Below 30.0 N — the static limit μs·N — friction returns exactly what is asked for and nothing moves, so the curve is the 45° line and the coefficient never appears. At that point the surface gives way and the force drops to μk·N = 22.5 N, where it stays however hard the block is pushed. The gap above the flat line is the surplus that accelerates it: 22.5 N at the right-hand edge of the axis.

Friction

  1. 1 The force that takes what it needs
  2. 2 The chatter a stiffer holder removes
  3. 3 The grip that is not a coefficient
  4. 4 The part of the wrap that is actually gripping
  5. 5 The grip that needs a little slipping
  6. +4 more
9 essays · mechanics What a passing wave does to a ring. A ring of 8 free masses at 4 phases of a passing gravitational wave, in both polarisations. The upper row is the + mode: one diameter lengthens while the perpendicular one shortens, and half a cycle later they swap. The lower row is the × mode, which is the same pattern rotated by forty-five degrees rather than ninety — the signature of a spin-2 field, and the reason a detector is built as two arms at a right angle. The drawn strain is 0.42; a real one is 10⁻²¹, so the deformation is exaggerated 4.2·10²⁰ times. At that true strain a four-kilometre arm changes length by 4·10⁻¹⁸ m.

Gravitational waves

  1. 1 The wave that stretches one way and squeezes the other
  2. 2 The orbit that has to shrink
  3. 3 What the instrument actually hears
  4. 4 A few cycles that are only mass and spin
  5. 5 The ring that does not come back
  6. +4 more
9 essays · astrophysics One parabola, several wells. Unlike potential wells, each divided by its own curvature at the bottom, against the single parabola ½x² drawn through all of them. They agree near the minimum because a function with a minimum has no linear term there, so the quadratic term is the first thing it has. The labels give where each well departs from the parabola by more than 1% of the parabola's own value there: a pendulum at 0.35, a chemical bond at 0.01, a pair of atoms at 0.0015. A symmetric well has no cubic term and stays close for a long way; a well that is steeper on one side than the other has one, and leaves the parabola almost at once — which is why those numbers differ by factors of hundreds and not by a few per cent.

Harmonic approximation

  1. 1 Every minimum is a parabola
  2. 2 The two pendulums that will not stop swapping
  3. 3 Why heating a perfect spring changes nothing
  4. 4 The oscillator that answers at three times the question
  5. 5 The spectrum that weighs a bond
  6. +4 more
9 essays · mechanics Why a straight front stays straight. A plane wavefront, with 9 points on it treated as sources and a wavelet of radius vt drawn about each. The envelope of those circles — the curve touching all of them — is a second straight line, parallel to the first and displaced by exactly vt. That is the whole of straight-line propagation: nothing else has to be assumed, and in particular nothing has to be said about rays, which are afterwards defined as the normals to these fronts. The construction is drawn with the wavelets left in, because they are the part that does the work.

Huygens

  1. 1 Every front is a source
  2. 2 The spiral that says how much light arrives
  3. 3 The wave that comes from the rim
  4. 4 The backward wave Huygens had to remove
  5. 5 The fan of plane waves inside every beam
  6. +4 more
9 essays · waves Reflected upside down. A pulse arriving at a join where the impedance rises by a factor of 3, drawn at three moments. The amplitudes are read off the marched wave: the reflected pulse is -0.500 of the incident one and the transmitted pulse is 0.500, against (1−Z₂/Z₁)/(1+Z₂/Z₁) = -0.500 and 2/(1+Z₂/Z₁) = 0.500 from the two matching conditions. The reflection is inverted, which is the same fact as a pulse on a string flipping when it reaches a wall: a wall is a medium of infinite impedance, and the inversion is what keeps the displacement at the join equal to zero. Note that the transmitted amplitude exceeds one where the second medium is lighter, and that this is not a violation of anything: amplitude is not energy.

Impedance

  1. 1 What happens where the medium changes
  2. 2 The layer that makes a reflection vanish
  3. 3 The taper that matches every note
  4. 4 The mismatch no network can remove
  5. 5 The absorber whose bandwidth is its thickness
  6. +4 more
9 essays · waves A loop leaving the field. A rectangular loop of wire 0.3 metres by 0.2 metres moving at 1.5 metres per second out of a region of magnetic field of 0.6 tesla directed into the page, marked with crosses. 0.08 metres of the loop's width is still inside the field. The induced current runs clockwise, and the force on the side that is in the field opposes the motion.

Induction

  1. 1 The field that makes the other, and only while it is changing
  2. 2 The magnet that falls slowly
  3. 3 The rule that is two laws wearing one coat
  4. 4 The coupling that is the same both ways
  5. 5 The circuit that fights its own change
  6. +4 more
9 essays · electromagnetism The field of a current loop, seen edge on. Magnetic field lines integrated from the Biot–Savart law for the current shown. Every line closes on itself: there is nowhere for one to start and nowhere for it to end, because no magnetic charge exists to end on.

Magnetism

  1. 1 The field with no ends, and the force that does no work
  2. 2 The force that does no work
  3. 3 The loop that behaves like a needle
  4. 4 The drift that does not care what the charge is
  5. 5 The current no particle carries
  6. +4 more
9 essays · electromagnetism The frequencies a repeat will not carry. The band structure of a medium made of quarter-wave layers of index 1 and 2, repeated for ever: frequency against Bloch phase across one cell, in the reduced zone. Inside a band the phase runs from 0 to π and the wave travels. Between bands there is no real phase at all, and the shaded strips are frequencies at which the medium supports nothing — not a weakly transmitted wave, no wave. Gap 1 runs from 0.784 to 1.216; Gap 2 runs from 2.784 to 3.216, in units of the quarter-wave design frequency. The first, measured off the drawn band edges, is 0.4327 wide against the 0.4327 of (4/π)·arcsin|r| — the same number computed from the Fresnel ratio of the two indices alone, agreeing to 2.6e-14 per cent. Every band edge sits where the phase is 0 or π, which is to say where the wave's own period fits the repeat a whole number of times: the gap is a property of the periodicity, and the materials only decide how wide it is.

Periodic media

  1. 1 The gap a repeat opens
  2. 2 The mode that lives in the mistake
  3. 3 The frequency a lattice cannot carry
  4. 4 The end that knows how the middle was cut
  5. 5 The mirror that works from every direction
  6. +4 more
9 essays · waves Trajectories at one speed and several angles. Projectile paths launched at the same speed and five different angles. The 45° launch travels furthest, and the 20° and 70° launches land in the same place.

Projectile

  1. 1 The angle that throws furthest, and why nobody notices
  2. 2 The angle that drag moves
  3. 3 Everywhere a throw can reach
  4. 4 One curve answers every slope
  5. 5 The best throw is a tangency
  6. +4 more
9 essays · mechanics A blackbody in every direction, at a different temperature in each. The spectrum of a blackbody at 100 kelvin in its own frame, seen by an observer it is moving past at 0.5 of the speed of light, in 5 directions. Each curve is a Planck spectrum exactly — the Planck form survives a Doppler shift, with the temperature multiplied by the shift — and the temperatures run from 57.74 kelvin looking one way to 173.21 looking the other. So the body is a perfect blackbody in each direction and has no single temperature. A thermometer placed in the radiation reads something between, and what it reads depends on where it is put and on how much of the sky it sees — which is the reason a transformation law for temperature was argued about for sixty years without being found.

Relativistic thermodynamics

  1. 1 The body that has no temperature when it moves
  2. 2 The count that no observer can disagree about
  3. 3 The bath that pushes back
  4. 4 The column that is hotter at the bottom
  5. 5 The heat that turns into matter
  6. +4 more
9 essays · relativity Four answers to one push. Shear stress against shear rate for four fluids. The straight line through the origin is the Newtonian definition and is the only one of the four for which the word viscosity names a number. The Bingham fluid does not move at all until the stress passes 0.4, which is why toothpaste holds a shape on a brush and why wet concrete can be stood in a heap.

Rheology

  1. 1 The fluid that answers back
  2. 2 The liquid that remembers
  3. 3 The paste that holds up its own hill
  4. 4 The liquid that climbs the rod
  5. 5 The stretch a chain cannot outrun
  6. +4 more
9 essays · fluids The screening that survives to zero frequency. How far a magnetic field gets into copper against how fast it is changing, drawn beside the London depth of a superconductor with a carrier density of 6.0e+28 per cubic metre. The metal's curve falls as one over the square root of the frequency — measured on the drawn curve as -0.5000 against −½ — and it is a straight line on these axes with no bottom: at a hundred hertz the field reaches nine millimetres in, and at zero frequency it reaches all the way through, because a normal metal screens by dissipating and a steady field dissipates nothing. The superconductor's line is flat at 21.7 nanometres. The frequency does not appear in the expression for it, so there is nothing for it to depend on, and the screening is as complete at zero frequency as at any other. The two lines cross at 9.0e+12 hertz, in the far infrared, and above that the ordinary metal is actually the better screen — which is a useful corrective, because a superconductor's advantage is not that it screens harder but that it does not need the field to be changing. What the picture cannot show is where the flat line stops: above the energy gap the pairs break, the superconductor becomes an ordinary metal, and the flat line turns into a sloping one.

Superconductivity

  1. 1 The field that is pushed out
  2. 2 The two in the flux quantum
  3. 3 Two lengths, and which one is longer
  4. 4 The voltage that is a frequency
  5. 5 The circuit that forgets its charge
  6. +4 more
9 essays · electromagnetism Two sources 3 wavelengths apart. Circular 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.

Superposition

  1. 1 When two waves meet, they simply add
  2. 2 What adding does to the energy
  3. 3 The one medium that was supposed to add exactly
  4. 4 The phases that turn a glow into pulses
  5. 5 The lattice no phase can bend
  6. +4 more
9 essays · waves Each stage takes 25.0 per cent of what is left. Entropy against temperature for a spin-½ paramagnet at 0.25 T and 1 T, with the cooling cycle drawn between them: a vertical drop is isothermal magnetisation, a horizontal move is adiabatic demagnetisation. Starting from 1 K the treads are at 1.000 K, 0.250 K, 0.062 K, 0.016 K, 3.91 mK. Each is 0.2500 of the one before — a ratio read back off the drawn treads rather than written into them, and equal to the field ratio 0.25/1 because this refrigerant's entropy depends on the field and the temperature only through their quotient. The steps therefore shrink in proportion to what is left, and no finite number of them arrives.

Third law

  1. 1 The staircase that never reaches the floor
  2. 2 The entropy that is still there at zero
  3. 3 Hotter than any temperature there is
  4. 4 The entropy that depends on how fast it was cooled
  5. 5 A law about spectra, not about heat
  6. +4 more
9 essays · thermodynamics The critical angle for n = 1.5 into n = 1. Refracted 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.

Total internal reflection

  1. 1 The angle past which light cannot leave
  2. 2 The reflection that happens where the glass is not
  3. 3 The angle at which total reflection stops being total
  4. 4 The corner that sends light home
  5. 5 The window a diamond is cut inside
  6. +4 more
9 essays · optics A packet on deep water, ω = √(gk), 1.6 s apart. A wave packet built from a Gaussian spread of wavenumbers about 1.57 per metre, drawn at two times 1.6 seconds apart, with its computed envelope ghosted around it. Between the two frames the envelope's peak moves 2.01 metres and the marked crest moves 3.95 metres, so the packet travels at 1.26 metres per second and the crests at 2.47 — a ratio of 0.51.

Wave packets

  1. 1 The packet that moves at another speed than its own crests
  2. 2 The speed that depends on the length
  3. 3 The packet that will not keep its shape
  4. 4 The speed that carries no signal
  5. 5 The pulse two failures keep alive
  6. +4 more
9 essays · waves Four paths, one answer. The field of a straight wire carrying 10 A, summed step by step around four closed paths in 4000 pieces each. Three of them enclose the wire and each returns 12.566 µT·m, which is μ₀I; the fourth does not enclose it and returns zero, because the outward stretch of the path and the return stretch cross the same field lines in opposite senses. Nothing about the shape survives into the answer — not the radius, not the centring, not the corners — which is what makes the law usable and also what makes it useless without a symmetry to hand.

Ampere law

  1. 1 The field that wraps a current
  2. 2 The field outside the solenoid, which is not zero
  3. 3 The law that is always true and rarely useful
  4. 4 The field that points against the magnet it is in
  5. 5 A potential that does not come back to itself
  6. +3 more
8 essays · electromagnetism

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