Time dilation - Lorentz transformation using light clock

[kapitan90]

Homework Statement

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)

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
$$t'=t/\sqrt{1-v^2/c^2}$$

Homework 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

 

[Doc Al]

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?

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.)

 

[kapitan90]

Ok, now it works, thanks for your reply!