To understand length transformation starting from relativity postulates. In this problem we calculate the length of a light clock that moves at speed v parallel to its axis in the moving system. A light clock ticks every time light makes a round trip between two mirrors separated by a distance L. The key point is that we can deduce the length of this clock directly from the postulates of relativity: The laws of physics are the same in any coordinate system that moves at constant velocity (i. e., any inertial reference frame). The speed of light is c when measured with respect to any coordinate system moving at a constant velocity. The light clock is based on the propagation time of light between mirrors spaced a distance L apart (in the rest frame of the clock). As the light pulse bounces back and forth between the mirrors, a small part of it is allowed to escape through the partially silvered mirror on the left. These small transmitted pulses of light hit a detector, which therefore emits "ticks" evenly spaced (in time) by one round-trip time of the pulse. (New pulses are injected in phase with the detected pulses to keep the clock going.)

a. What is the period t0 between successive ticks of the clock in its rest frame?
b. Use time dilation to determine the time tS between the ticks of the light clock as viewed from reference frame S.
c. What is the round-trip time tS?
d. What is the length LS of the clock according to a stationary observer in S?