In this problem, we show that the clock's length appears shortened when viewed from a reference frame S in which the clock is moving with relative speed vv to the right, parallel to its long axis. The key is to calculate explicitly the length of time that an observer in S will measure between "ticks" of the moving clock in terms of LS$,$ the length of the clock in the S frame. Comparing this with the known period of the clock in the S frame allows us to compute the length of the clock in the S frame. Einstein used gedanken experiments such as this to clarify his thinking as he strove to remove inconsistencies from the basic formulations of physics.What is the period t$0$ between successive ticks of the clock in its rest frame?

Express your answer in terms of variables given in the introduction. Use c for the speed of light.

Use time dilation to determine the time tS between the ticks of the light clock as viewed from reference frame S$.$

Express the time tS between these ticks in terms of LL$,$ the relative speed vv$,$ and the speed of light c

What is the round$-$trip time tStS$?$

Use kinematics to express tStS in terms of LSLS$,$ the velocity vv$,$ and the speed of light cc$.$