I want to ask that in vacuum or any other medium can light reflect itself ? I an asking for visible light in the spectrum but of any other light does so please answer .
Can light reflect light ... I [am] asking for visible light
No, light waves pass straight through other light waves. This is one of the first things you are taught about light in any school-level physics course.
The fact that two waves continue on their way when they have passed through each other as if there had never been an encounter will come as no surprise to students who have:
- closely observed raindrops falling in a puddle, or
- thought about the fact that signal-carrying microwaves and radio waves pass through each other constantly, particularly in cities dense with communications.
Still it is remarkable.
Physics being what it is, there are some ideas that can serve to confuse ...
a new analysis in Physical Review Letters shows that the Large Hadron Collider (LHC) at CERN could detect around 20 photon-photon events per year.
The question asks about "visible light", so that would be light of the sort directly visible to humans.
20 events a year is pretty few and I imagine the conditions in the LHC, when operating, are pretty far from the sort of conditions living humans should place their eyeballs into.
To create an electron-positron pair, the total energy of the photons must be at least $2m_ec^2$ = 2 × 0.511 MeV = 1.022 MeV (me is the mass of one electron and c is the speed of light in vacuum), an energy value that corresponds to soft gamma ray photons.
AFAIK visible light doesn't include soft gamma rays.