Theoretically if you passed the speed of light in a medium, would there be a sonic boom equivalent? I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object travelling would reach infinity. However in a medium, would there be some sort of theoretical equivalent to a sonic boom that would occur? Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky? 
 A: To leave an answer that addresses the question, which was answered in comments but comments are not permanent here:

in a medium, would there be some sort of theoretical equivalent to a sonic boom that would occur?

It is called Cerenkov radiation and it is continually utilized in high energy physics detectors and cosmic ray experiments.

It is  the electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The characteristic blue glow of an underwater nuclear reactor is due to Cherenkov radiation.

You ask:

Since sonic booms are formed when sound waves can't catch up with an object, could the same happen with light waves? Would it look like an immense burst of light in the sky? 

Light waves are built up in synchrony by a large number of photons. Cerenkov radiation is radiation from one elementary point particle one photon at a time, and the build up into light one sees here :


NRC photo of Cherenkov effect in the Reed Research Reactor.

comes from innumerable electrons with random directions exceeding the speed of light in the medium.
The sonic boom comes from one airplane , a single electron emits Cerenkov radiation  practically continuously on its path, similar to the energy dissipation of the sonic boom, but the electron "boom" is a whisper as far as detectors go.
An interesting aside: a veteran particle physicist of the first days of creating beams and experiments, told me that he centered the beam by the Cerenkov light in his eyes.
