**Experiment 5****:** A light clock lies on its side on a railroad
car as the car moves to the left with velocity v.

__Question__: How is the length of the clock affected?

__Answer__: We know that the time between ticks on the moving clock,
as we see it, will be t´ = . Let,

t

_{1}= time that takes the light to go from the first mirror to the second , as we perceive it.

t_{2 }= time that it takes the light to go from the second mirror back to the first, as we perceive it.

L´= length of the light clock, as we perceive it.

We can analyze the situation as follows:

From the above picture we see that the distance the light traveled in time
t_{1} was L´+ vt_{1}. However, this distance is also
equal to ct_{1} (rate **x** time). Also, the distance the light
traveled on the return trip was L´- vt_{2} = ct_{2}.
Solving for t_{1}, we have

which implies that L´= ct

which implies L´= (c - v)t

which implies t

Similarly,

which implies that L´= ct

which implies L´= (c + v)t

which implies t

Thus,

=

=

=

which implies that = .

Since t = (2L)/c,

which implies that = ,

which implies = ,

which implies = ,

which implies L´ = L .

__Conclusion__: Since is less than 1, this shows that we will measure
the length of his light clock as being less than ours. Thus, when an object
is moving in a straight line with a fixed velocity v, we will see its length,
as measured in the direction in which it is moving, shorten.