wave speed from frequency and wavelength

period and frequency

intensity: power per area the wave passes through

$v = \sqrt{\dfrac{T}{\mu}}$

speed of a wave on a string ( $T$ = tension, $\mu$ = mass per unit length)

fundamental mode of a string fixed at both ends (nodes $\tfrac{\lambda}{2}$ apart)

$n_1 \sin\theta_1 = n_2 \sin\theta_2$

Snell's law at a boundary

refractive index from the speed of light in the material

$\sin C = \dfrac{1}{n}$

critical angle, going from the material into air

power of a lens in dioptres ( $f$ in metres)

$\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f}$

magnification from image and object distances

$n\lambda = d\sin\theta$

diffraction grating: order $n$ , slit spacing $d$

energy of a photon ( $h$ = Planck constant)

$hf = \phi + \tfrac{1}{2}mv_{\text{max}}^2$

photoelectric effect ( $\phi$ = work function)

$\lambda = \dfrac{h}{p}$

de Broglie wavelength of a particle with momentum $p$

$1\,\text{eV} = 1.6\times10^{-19}\,\text{J}$

converting electronvolts to joules

$I = \dfrac{\Delta Q}{\Delta t}$

current is the rate of flow of charge

potential difference: energy transferred per unit charge

drift velocity $v$ ( $n$ = charge carriers per unit volume)

resistance (Ohm's law when $R$ is constant)

$R = \dfrac{\rho l}{A}$

resistance of a wire from resistivity $\rho$ , length and area

$P = VI = I^2R = \dfrac{V^2}{R}$

$R = R_1 + R_2 + \dots$

$\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$

$\varepsilon = I(R + r)$

e.m.f. with internal resistance $r$

$V = \varepsilon - Ir$

terminal p.d. drops as current rises

$V_{\text{out}} = \dfrac{R_2}{R_1 + R_2}V_{\text{in}}$

thin lens equation (real-is-positive)

resistors in parallel

potential divider output across $R_2$

Waves and Electricity

Key equations

2.1Progressive waves

2.2Superposition and stationary waves

2.3Refraction, total internal reflection and polarisation

2.4Diffraction and interference

2.5Wave–particle duality and the photoelectric effect

2.6Charge, current and potential difference

2.7Resistance, resistivity and circuits

2.8EMF, internal resistance and potential dividers