I've just studied Einstein's Special Theory of Relativity and have followed most part of it. I was just wondering that whether the equations of Lorentz transformation are applicable on light? i.e. can we consider a surface as system ($K$) and the light ray striking it as ($K'$) and then use $v=c$?
Does it have anything to do with the fact that the speed of light is not relative?
The Lorentz transformations are used to transform between different inertial frames. For example if you and I are in relative motion then the Lorentz transformations convert the positions of spacetime points in my rest frame to the positions of spacetime points in your rest frame.
However anything travelling at the speed of light has no rest frame, so the Lorentz transformations cannot be used. If you attempt to use them you will find the transformation becomes singular - more specifically the Lorentz factor $\gamma \rightarrow \infty$.
This does not mean light does not obey the equations of relativity. Quite the reverse, because all the machinery of relativity (both special and general) can be applied to light to calculate its world lines. In fact the world lines that light travels on are important geometrical properties called null geodesics.
