What was the primary difficulty in establishing the wave theory of light,and who explained it?

(N/A) The primary difficulty in establishing the wave theory of light was that,since waves traditionally required a medium for propagation,it was unclear how light waves could travel through a vacuum.
James Clerk Maxwell resolved this by developing a set of equations describing electricity and magnetism. From these equations,he derived a wave equation that predicted the existence of electromagnetic waves.
Maxwell calculated the speed of these electromagnetic waves in free space and found that the theoretical value matched the measured speed of light. Consequently,he proposed that light is an electromagnetic wave.
According to Maxwell,light waves consist of oscillating electric and magnetic fields. $A$ changing electric field generates a time-varying magnetic field,and a changing magnetic field generates a time-varying electric field. This self-sustaining process allows electromagnetic waves to propagate through a vacuum without a material medium.
While ray optics (based on rectilinear propagation) explains phenomena like reflection and refraction,wave optics explains phenomena like diffraction and interference,where light bends around obstacles comparable in size to its wavelength (approximately $0.5 \ \mu m$).