- #1

Chewy0087

- 368

- 0

## Homework Statement

Show the derivation for legnth contraction, given that from the example given;

The example shows a moving light clock - two walls which are moving in a direction at speed u and a beam of light from wall A to wall B then back to A and so forth.

From Ao (starting point) to B1 (distance moved after the beam has got there)

=t1 = "Moving" legnth / c - u

And from B1 - A2

t1 (2) = "Moving" Length / c + u

## Homework Equations

t subscript 1 = 2L / c * sqroot (1 - u²/c²)

Basically the time dilation equation is given (and i managed to work out in an earlier question)

## The Attempt at a Solution

Well I added up t1 and t1 (2), to get the time taken by the light to do one back and forth getting;

t1 + t1(2) = gamma*time = 2 * Moving Length / c*(1- u²/c²)

Making Moving length the subject;

Moving Length = (c*(gamma*time))*(1-u²/c²)

Put gamma into the equation;

Moving Length = (c/2)*(1-u²/c²)*2L/(c*sqrt(1-u²/c²))

And from here I'm totally stuck, I do know that the final answer is "Normal" length / gamma but really stuck taking the final steps... :/

Any help would be appreciated