Relative velocity of light beams Assume two light beams moving in the same direction 
i want to use the  relativistic velocity transformation equation to find the relative velocity with each other,
Note : i let $C$=1
$V_{ab}$=$\frac{V_{a}-V_{b}}{1-V_{a}V_{b}}$
when i put $V_{a}$=$V_{b}$=1 the limit is $\frac{0}{0}$
though i expected to get $C$
Also used that website to get the limit told me
Limit Does not exit.
 A: Special relativity does not tell you, that there are inertial systems moving along with a light ray. The formula for velocity addition is essentially a formula about transformation of a velocity in the frame of a moving observer. 
It's just not the right question to ask, what an observer moving at $c$ would observe. Since there are none. 
A: The velocity addition formula applies when there are two observers (say A and B) moving with respect to each other.  If C is some other object, we have three relevant velocities:  That of B as measured by A, that of C as measured by B, and that of C as measured by A.
But in your setup there is only one observer.  (A light beam is not an observer; it has no inertial frame).  So the velocity addition formula does not apply.
A: The answer is C.  Light travels at C, the speed of light, for any and all observer velocity.  That is your formula for relative velocity assumes time is a constant for all observers, but this assumption is invalid for your hypothetical.  For classical physics, time is nearly constant (or at least a good enough approximation), but it not EXACTLY true and fails as one approaches the speed of light.  For all observers approaching the speed of light, time slows down, and thus light continues to appear to be moving a speed C.
Funny story, this nearly exactly the question Einstein was trying to answer when he postulated and proposed special relativity.  In your hypothetical, (lets suppose each beam of light was able to "observe"), if a beam of light (or more accurately, the source of a beam of light) appeared to slow down, said beam of light would stop looking like a beam of light.  This is a contradiction of the nature of light; hence, Einstein concluded, through mathematics of course, that time must change for the moving observer (or source of light) so that light ALWAYS appears to be moving at C, his "Principle of Invariant Light Speed"
