Maxwell came up with a couple equations pertaining to light:
1) some kind of charge-field relation that involves calculus.. not in the scope of AP
2) magnetic fields have no beginnings or ends, whereas electric fields do
3) change in magnetic field generates an electric field
4) a current or change in electric field generates a magnetic field
An electromagnetic wave is essentially energy transmitted through fields. Change in magnetic field causes change in electric field by Faraday's Law, then the change in electric field causes a magnetic field by Ampere's Law, that may change the existing magnetic field or not.
I forgot to label the third picture; the vertical waves are electric fields and the horizontal waves are magnetic fields.
Since light rides on electromagnetic fields, it does not rely on a medium, thus explaining how it can travel through a vacuum. The constancy of the speed of light also relies on this fact; light is not something that you actively move, but rather it is something you send through a field.
If the speed of light is your cake, the derivation of Lorentz Transformation might be of interest.
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