Just like water waves are disturbances on the surface of the ocean, and sound waves are pressure variations in the air so are electromagnetic waves which are disturbances in the electromagnetic field. An electromagnetic wave is a collection of oscillating electric and magnetic fields, propagating perpendicular to each other.
Electromagnetic waves can be described by Maxwell's Equations which in general describe the behavior of the electric and magnetic fields, and are what is known as transverse waves. Transverse waves are waves whose direction of propagation is perpendicular to the direction of disturbance in the medium. In the figure above you can see that the magnetic field oscilates left and right and the electric field oscilates up and down while the wave propagates forward, perpendicular to both.
This is in constanst to what is known as longitudinal waves which are waves whose direction of propagation is aligned with the direction of disturbance (like sound waves).
Perception of light
since light is a wave, it can be described mathermatically by a cosine with an amplitude of the electric field. Since the electric and magnetic fields are always perpendicular (in free space) one can get away with describing the behavior of only one of the field. Most commonly electromagnetic waves are described by the electric field - E.
where k is determined by the wavelength and both k and omega are related by the dispersion relation through ther speed of light.
The wavelength of an electromagnetic wave corresponds to the color that we perceive. For wavelengths between approximately 370-740 electromagnetic radiation is within the optical spectrum and is what we usually refer to as light. wavelengths around the 740 nanometers are the red end of the visible spectrum and those around 370 are the violet end of it. Longer wavelength begin with the infrared and become as long as kilometers as radio waves. And shorter wavelenths begin with the ultraviolet (the reason we put sunscreen in the beach) and go as short as gamma rays which is violent radiation emitted by supernovas in space.
We also have to understand that the light we see in our eyes is not simply the electric or magnetic fields, but rather their intensity which is just the modulus squared of the field
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