Light is an electromagnetic wave, and its interaction with matter is described by a small number of rules. When light strikes a smooth surface such as a mirror, it reflects such that the angle of incidence equals the angle of reflection. When light passes from one medium into another, it changes speed, and this speed change causes the light to bend at the interface. This bending is called refraction, and it is described by Snell's law, \(n_1\sin\theta_1 = n_2\sin\theta_2\), where the indices \(n\) are the refractive indices of the two media. The photoelectric effect, in which light shining on a metal ejects electrons, provided crucial evidence that light can behave as discrete packets of energy called photons, with each photon's energy given by \(E = hf\), where \(h\) is Planck's constant and \(f\) is the frequency.
Electricity describes the behavior of electric charges, which come in two types, positive and negative, and are conserved in all interactions. The fundamental force between two point charges is given by Coulomb's law, \(F = kq_1q_2/r^2\), with \(k = 9 \times 10^9 \text{ N·m}^2/\text{C}^2\); the force is repulsive for like charges and attractive for unlike ones. An electric field \(\vec{E}\) at a point in space is defined as the force per unit positive test charge at that point, and for a single point charge it is \(\vec{E} = kq/r^2\) in the radial direction. The electric potential \(V\) at a point is the work per unit charge required to bring a test charge from infinity to that point, and the potential energy of a charge \(q\) at a point is \(U = qV\).
Electric current is the rate of flow of charge, \(I = \Delta Q/\Delta t\), measured in amperes, and conventional current is taken to flow from positive to negative potential. Ohm's law relates the voltage across a resistor to the current through it as \(V = IR\), where \(R\) is the resistance in ohms. In a series circuit, the same current flows through every component and the voltages across components add, while in a parallel circuit, the same voltage appears across each branch and the currents add. A magnetic field \(\vec{B}\) exerts forces on moving charges and on current-carrying wires, with directions given by the right-hand rule and measured in teslas. Faraday's law of induction states that a changing magnetic flux through a loop induces an electromotive force, \(\mathcal{E} = -d\Phi_B/dt\), the operating principle behind electric generators. Modern physics extends classical understanding in two major ways. Special relativity rests on two postulates: the laws of physics are the same in all inertial reference frames, and the speed of light in vacuum, \(c\), is the same for all observers regardless of the motion of the source. From these postulates follow remarkable effects such as time dilation, in which a moving clock runs slow by a factor of \(1/\sqrt{1 - v^2/c^2}\), so that \(\Delta t = \Delta t_0/\sqrt{1 - v^2/c^2}\), where \(\Delta t_0\) is the proper time measured in the clock's own rest frame.