Length Contraction

 Length contraction:

The length of a rod as measured in a frame of reference, at rest with respect to the observer , is called its proper length and obviously be the same in all stationary frames of reference. It is only in moving reference frames that it will be different ,depending upon their relative velocities with respect to the observer. 

We can see that faster the motion of the rod, with respect to the observer, shorter its length compared with the proper length. 

Similarly if v=c, i.e., if the rod moves with the velocity of light(c), its length would be zero. It is also obvious that any object in a state of rest will have the largest proper length. If an object lies along y-axis or z-axis perpendicularly to the direction of motion, then their will be no shortening of length. If the rod is slightly  tilted,  their will be slightly shortening of length. This phenomenon of shortening of length is also called as the Lorentz - Fitzgerald contraction. Also one important things to be noted that the rod in motion appears to be shorter with respect to an observer at rest and also the observer's length also appear to be shorter with respect to the moving rod. It is called the reciprocity of the contraction.