What was the difficulty in established the wave theory of light and who explained it ?

Explanation

The only major difficulty in established the wave theory of light was that since that a wave required a medium for its propagation how could light waves propagates through vacuum ?
Maxwell had developed a set of equations describing the laws of electricity and magnetism and using these equations he derived the wave equation from which he predicted the existence of electromagnetic waves.
From the wave equation, Maxwell calculate the speed of electromagnetic waves in free space and he found that the theoretical value was very close to the measured value of speed of light. From this he propounded that light must be an electromagnetic wave.
Thus, according to Maxwell, light waves are associated with changing electric and magnetic fields.
Changing electric field produces a time and space varying magnetic field and a changing magnetic field produces a time varying electric field.
This changing electric and magnetic fields result in the propagation of electromagnetic waves even in vacuum.