# Homework Help: Time dilation - Lorentz transformation using light clock

1. Apr 10, 2012

### kapitan90

1. The problem statement, all variables and given/known data
I am trying to derive the time dilation formula using Pythagorean theorem:
L = ct (in clocks rest frame)
D = ct'(in observer's frame, the clock moving with velocity u)

3. The attempt at a solution

So $$D^2 = L^2 +v^2t^2$$
$$c^2{t'}^2=c^2t^2+u^2t^2$$
So$$t'=t*\sqrt{1+v^2/c^2}$$
but it should be
$$t'=t/\sqrt{1-v^2/c^2}$$

2. Relevant equations
This would work if D=ct, not ct' and L=ct', but I guess it isn't right with my choice of frames of reference?

Sources: http://www.drphysics.com/syllabus/time/time.html

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2. Apr 10, 2012

### Staff: Mentor

You're mixing up your frames a bit. The clock moves a distance vt' (not vt) in the observer's frame. (The observer uses his own time measurements, of course.)

3. Apr 10, 2012