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. As shown in the figure (Figure 1) , 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.)
Part C
What is the round-trip time tS?
Use kinematics to express tS in terms of LS, the velocity v, and the speed of light c.
Part E
Notice that the clocks at the front and rear mirrors of the light clock do not show the same time when viewed from the moving frame. Why is this?
a)The front clock experiences a greater time dilation because it moves ahead of the rear clock
b)The clocks start simultaneously in the rest frame, so they cannot start simultaneously in the moving frame.
c)Since the light clock is passing the observer, the signal from the front clock takes longer to reach the observer, making the time appear earlier.