# Derive length contraction formula given a two system experiment.

**1. The problem statement, all variables and given/known data**

Show that the experiment depicted in Figure 2.11 and

discussed in the text leads directly to the derivation of

length contraction.

Figure 2.11:

**2. Relevant equations**

d=v*t

Requested result: L=L_{0}[itex]\sqrt{1-\frac{v^2}{c^2}}[/itex]

**3. The attempt at a solution**

In K the distance the light pulse travels is 2t_{1}v+L and the total time for the pulse to return to its origin is that distance over c.

In K’ the distance the light pulse travels is 2L_{0} and the total time for the pulse to return to its origin is that distance over c.

I can also say that t_{1}=[itex]\frac{vt_1+L}{c}[/itex] then solve for t_{1} to substitute that into total time in K frame. At this point I’m not sure where to go or even if what I’ve done is useful. I am tempted to set the total times equal to one another and solve for L but I when I’ve tried this I can get it to look like it is supposed to although there are familiar pieces.

Any suggestions? Thank you!

http://ift.tt/1cToVJn

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