Q. What do you mean by Length Contraction?
The length of any object in a moving frame will appear for shortened in the direction of motion. The amount of contraction can be calculated from the Lorentz transformation. The length of the object is maximum in the frame in which it is at rest. Let us consider two inertial frames of references S and S' where the axes, x and x', y and y' and z and z' are parallel and the origin O' of frames S' is moving with a uniform velocity v with respect to frames S as shown in fig. Suppose a rod is placed along X' axis in moving frame S'. An observer O' in this frame observes the coordinates of the two ends of the rod at X1' and X2' respectively. This rod will always appear at rest to observer O' in frame S' and the measurement of the position of the two ends will not depend on the time. The length measured in such a frame is constant and known as proper length. The frame S' in which the rod appears at rest, is called proper frame and the length observed in this frame is called proper length. Then the proper length of the rod suppose x2 & x1 are the positions of the two ends of the rod as observed simultaneously at time ‘t' in the frame S. the observed length of the rod in frame S will be. Hence the length is appeared to be constricted, by the factor. This contraction in length of a body along the direction of motion is also called Lorentz Fitzgerald contraction.