Electromagnetic wave (light) propagation

I think the easiest way to explain it is like a ripple in a pond: When an electron transitions energy levels, the lost energy is emitted as a photon. - think of it like touching the surface of water. The initial disturbance results in a wave that propagates away from the source.
The speed in a water wave depends on things like amplitude and density and so forth, but this is not the case for light.
However, the speed is dependent on permittivity and permeability... I believe in a diamond light travels around half the speed it does in a vacuum.
The Aether theory was popular but has been disproved, so it is believed light does not need a medium.
I can offer equations to model it, but I cannot provide a physical interpretation of why they work.

 

Wave behaviour arises when the second spatial derivative of some quantity (in the case, say an Electric field) is proportional to the second time derivative of the said quantity.

One of the triumphs of Maxwell's equations was to prove this relationship for E and B fields. Not only did this show that EM waves exist, it correctly predicted the velocity of these waves.

From a laymans perspective though, it is helpful to remind yourself what an E-field actually is. It is a "map" of how the electrostatic force affects a one Couloumb charge throughout space. Imagine two spatially separated charges. If you were to wiggle one charge up and down, the other charge would invariably move via Couloumbs Law, causing it to wiggle as well. This transfer of energy and momentum is essentially described by an EM wave.

Claude.