Electromagnetic Radiation

Introduction

Electromagnetic radiation is a transverse energy wave that is composed of an oscillating electric field component, E, and an oscillating magnetic field component, M. The electric and magnetic fields are orthogonal to each other, and they are orthogonal to the direction of propogation of the wave. A wave is described by the wavelength, , which is the physical length of one complete oscillation, and the frequency, , which is the number of oscillations per second. The figure shows one wavelength of a wave of light. The names we give electromagnetic radiation for different wavelength and frequency ranges are listed in the electromagnetic spectrum document. Schematic of an electromagnetic wave

Velocity of light

Electromagnetic waves travel through a vacuum at a constant velocity of 2.99792x108 m/s, which is known as the speed of light, c. The relationship between the speed of light, wavelength, and frequency is:

c = 

When light passes through other media, the velocity of light decreases. For a given frequency of light, the wavelength also must decrease. This decrease in velocity is quantitated by the refractive index, n, which is the ratio of c to the velocity of light in another medium, v:

n = c / v

Since the velocity of light is lower in other media than in a vacuum, n is always a number greater than one. The table lists the refractive index of several examples. Refractive index is an intrinsic physical property of a substance, and can be used to monitor purity or the concentration of a solute in a solution. The refractive index of a material is measured with a refractometer, and is usually made versus air. If the precision warrants, the measurements can be corrected for vacuum. Note that the difference between nair and nvacuum is only significant in the fourth decimal place.

For anisotropic materials, such as quartz crystals, light of different polarizations (see below) will experience different refractive indices. These indices are called the ordinary refractive index, no, and the extraordinary refractive index, ne.
medium n*
air 1.0003
water 1.333
50% sucrose in water 1.420
carbon disulfide 1.628
crystalline quartz 1.544 (no)
1.553 (ne)
diamond 2.417
*measured with 589.3 nm light

Polarization

An incoherent light source, such as the hot filament of a light bulb, consists of multiple, randomly oriented light emitters, which produce electromagnetic waves with their electric-field vector oriented in all directions. The resulting light emission is called unpolarized light.

Linearly (or plane) polarized light is light in which the electric-field vector is oscillating in only one direction. Linearly polarized light is produced by isolating one orientation of the electric field with a polarizer, or from lasers that contain polarized optical components.

Circularly polarized light is light in which the electric field vector is rotating around the axis of light propogation. The electric field vector can rotate in either the right or left direction (as viewed in the direction of light propogation), and the light is called right circularly polarized or left circularly polarized, respectively.

Wave-particle duality

Electromagnetic radiation shows both wave and particle characteristics depending on how the radiation is observed. Einstein first postulated that the energy of radiation is quantized and that radiation is composed of energy packets that were later named photons. The energy, E, of one photon depends on its frequency (or wavelength):

E = h = hc /

where h is Planck's constant (6.62618x10-34 Js),  is the frequency of the radiation, c is the speed of light, and  is wavelength.

de Broglie equation

Moving particles; such as electrons, protons, and neutrons; have wave properties as described by the de Broglie equation:

= h / p

where  is wavelength, h is Planck's constant, and p is the momentum of the particle. Beams of particles can therefore show wave effects such as interference.