Length Contraction

Consider again two observers account of a single tick of a light clock, except now we lay the clock on its side and analyze the distance between the two mirrors.

We now analize the single tick of this clock, taking into account the time dilation effect as needed.

For the trip from the left mirror to the right we have:

For the trip from the right mirror to the left we have:

From the time dilation effect, we know that

and