- #1

Joeirvin

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## Homework Statement

I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage..

**2. Homework Equations / attempt**

Let:

c = velocity of light.

v = the velocity as observed from where time t is measured.

D = distance AB.

t = time light occupies to pass from A to B.

t1 = time light occupies to return from B to A.

Firstly we can see that

t= D/(c+v)

And

t1= D/(c-v)

So for the total distance,

t+t1=D/(c+v)+D/(c+v)

Make a common denominator and add the two fractions,

t+t1=(D(c-V)+D(c+v))/((c+v)(c-v))

Expand the brackets,

(Dc+Dv+Dc-Dv)/(c^2+cv-cv-v^2)

Simplify, cancel out where possible,

(2Dc)/(c^2-v^2)

And take out the factor of 2D

t+t1=2D(c/(c^2-v^2)) or 2D(1/(c-(v^2/c))

( I am unsure whether or not taking it that far is right yet..)

Above is where i have arrived and the next step i am supposed to arrive at..

2D (c^2 / (c^2 - v^2)) = 2D (1 + (v^2 / c^2)]

Any help asap please?

thankyou