THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Thin lens
An idealised lens thin enough to neglect the thickness for ray tracing. Obeys the thin-lens equation 1/f = 1/s_o + 1/s_i and the lensmaker's equation 1/f = (n−1)(1/R₁ − 1/R₂).
Threshold energy
The minimum incoming-particle energy required to produce a given set of final-state particles in a collision, consistent with conservation of four-momentum. Computed cleanly in the centre-of-momentum frame as the total rest energy of the products; in the lab frame, requires extra kinetic energy to satisfy momentum balance.
tidal force
The differential gravitational pull across an extended body; stretches along the line to the attractor and compresses perpendicular to it.
Time dilation
The relativistic effect that a clock measured by an inertial observer in motion ticks slower than an identical clock at rest in that observer's frame, by the Lorentz factor γ = 1/√(1 − β²). Symmetric between frames; not an illusion; verified by muon decay, atomic clocks, and GPS.
Timelike
A separation between two events with invariant interval s² > 0 — meaning a sub-c signal can connect them. Timelike-separated events have a frame-independent temporal order; proper time Δτ = √(s²)/c elapses on a clock travelling between them.
Toroid
A coil wound into a doughnut shape. Confines its magnetic field almost entirely to the interior of the doughnut: B = μ₀ N I / (2πr).
torque
The rotational analogue of force: τ = r × F; equals the rate of change of angular momentum.
Total internal reflection (TIR)
The 100% reflection of light at an interface from a denser to a less dense medium when the angle of incidence exceeds the critical angle θ_c = arcsin(n₂/n₁). The basis of optical fibres, binoculars, and retroreflectors.
Transformer
A two-coil magnetic device that converts AC voltage up or down by the turn ratio: V₂/V₁ = N₂/N₁. The enabler of the electrical power grid.
Transmission line
A pair of conductors (coax, twisted pair, stripline) carrying signals whose wavelength is comparable to or shorter than the line length. Governed by the telegrapher's equations rather than Kirchhoff's laws.
Transverse Doppler effect
The relativistic frequency shift observed when the source's velocity is purely perpendicular to the line of sight at the moment of emission. Reduces to f = f₀/γ — pure time dilation, with no classical Doppler contribution. The cleanest experimental test of time dilation.
Transverse electromagnetic wave
An EM plane wave in which both E and B oscillate perpendicular to the propagation direction k, and perpendicular to each other. The Gauss-law constraints ∇·E = 0 and ∇·B = 0 force the transverse structure in vacuum.
Turbulence
Fluid motion organised into nested vortices across a vast range of scales. The last unsolved problem of classical physics.
Turns ratio
n = N₁/N₂, the ratio of primary to secondary turn counts in a transformer. Sets the voltage step (V₁/V₂ = n), the current step (I₁/I₂ = 1/n), and the impedance step (Z_reflected = n²·Z_load).
vector
A quantity with both magnitude and direction; represented as an arrow and added tip-to-tail.
Vector potential
The vector field A whose curl gives the magnetic field: B = ∇×A. Lets you compute B from a scalar-like integral over the source currents.
velocity
The rate of change of position with respect to time; a vector in 2D and 3D, a signed scalar in 1D.
Venturi effect
The drop in static pressure observed when a fluid flows through a constricted section of pipe.
vis viva equation
v² = GM(2/r − 1/a) — gives the orbital speed at any distance r for an orbit with semi-major axis a.
Viscosity
A fluid's internal resistance to shear. For Newtonian fluids, shear stress = η·(du/dy). Unit: Pa·s.
Volt
The SI unit of electric potential difference. One volt equals one joule of work per coulomb of charge transported. Symbol: V.
Voltage divider
Two resistors in series between a voltage source and ground, with the output voltage taken at the midpoint. V_out = V_in · R₂/(R₁+R₂). The simplest non-trivial circuit.
Vortex
A coherent region of swirling fluid — the basic building block of turbulent and near-turbulent flow.
Wave equation
The linear PDE whose solutions are any right-mover plus any left-mover at speed v.
Wave packet
A localised wave formed by superposing many plane-wave components with a narrow band of wavenumbers.
Waveguide mode
A specific transverse field pattern that propagates along a waveguide without distortion, characterised by a propagation constant β and a cutoff frequency below which the mode is evanescent.
Wavelength
The spatial period of a wave — distance crest to crest, symbol λ.
Wavelength (EM)
The spatial period λ of an EM plane wave, the distance between successive points of equal phase. Related to frequency by λ = c/f in vacuum, λ = c/(nf) in a medium. Ranges from kilometres (longwave radio) to femtometres (gamma).
Wavenumber
k = 2π/λ, the spatial angular frequency of a wave, measured in rad/m. The wavevector k has magnitude k and direction along propagation. In spectroscopy, wavenumber often means k̃ = 1/λ in cm⁻¹.
Weak equivalence principle
The statement that gravitational mass equals inertial mass for any test particle, regardless of composition — equivalently, that all bodies in vacuum fall with identical acceleration. Galileo's Pisa-tower observation, Eötvös's torsion-balance precision result, and the MICROSCOPE 2017 satellite null result confirm it to ≲ 10⁻¹⁵.