Let K be the stationary frame and K' the frame that moves along with the rod.As seen from K:
The rod will be shorter and have a length
and moves at a velocity v to the right. Thus, the rod will pass the mark in a time interval,
As seen from K' :
The rod is stationary and has a length l but the mark moves with a velocity v to the left. Thus, the mark will pass the rod by in a time interval,
From (2) we have,
