Electromagnetic (EM) waves are changing electric and magnetic fields, transporting energy and momentum through space.  EM waves are solutions of Maxwell's equations, which are the fundamental equations of electrodynamics.  EM waves require no medium, they can travel through empty space.  Sinusoidal plane waves are one type of electromagnetic waves.  Not all EM waves are sinusoidal plane waves, but all electromagnetic waves can be viewed as a linear superposition of sinusoidal plane waves traveling in arbitrary directions.  A plane EM wave traveling in the x-direction is of the form
E(x,t) = Emaxcos(kx - ωt + φ),  B(x,t) = Bmaxcos(kx - ωt + φ).
E is the electric field vector, and B is the magnetic field vector of the EM wave. Â For electromagnetic waves E and B are always perpendicular to each other and perpendicular to the direction of propagation. Â The direction of propagation is the direction of E x B.
If, for a wave traveling in the x-direction E = Ej, then B = Bk and j x k = i. Â Electromagnetic waves are transverse waves.
The wave number is k = 2π/λ, where λ is the wavelength of the wave.  The frequency f of the wave is f = ω/2π, ω is the angular frequency.  The speed of any periodic wave is the product of its wavelength and frequency.
v = λf.
The speed of any electromagnetic waves in free space is the speed of light c = 3*108 m/s.  Electromagnetic waves can have any wavelength λ or frequency f as long as λf = c.
When electromagnetic waves travel through a medium, the speed of the waves in the medium is v = c/n(λfree), where n(λfree) is the index of refraction of the medium.  The index of refraction n is a properties of the medium, and it depends on the wavelength λfree of the EM wave.  If the medium absorbs some of the energy transported by the wave, then n(λfree) is a complex number.  For air n is nearly equal to 1 for all wavelengths.  When an EM wave travels from one medium with index of refraction n1 into another medium with a different index of refraction n2, then its frequency remains the same, but its speed and wavelength change.  For air n is nearly equal to 1.
horizontal rule
The electromagnetic spectrum
Electromagnetic waves are categorized according to their frequency f or, equivalently, according to their wavelength λ = c/f.  Visible light has a wavelength range from ~400 nm to ~700 nm.  Violet light has a wavelength of ~400 nm, and a frequency of ~7.5*1014 Hz.  Red light has a wavelength of ~700 nm, and a frequency of ~4.3*1014 Hz.
Visible light makes up just a small part of the full electromagnetic spectrum. Â Electromagnetic waves with shorter wavelengths and higher frequencies include ultraviolet light, X-rays, and gamma rays. Â Electromagnetic waves with longer wavelengths and lower frequencies include infrared light, microwaves, and radio and television waves.
