Derivation of Relativistic Doppler Shift: Step-by-Step Guide

[applied ahmed]

i need thee the derivation of relativistic doppler shift. i found its derivation in the book of Serway, but it is not in detail and step by step.
in the book there is given that:

can anyone give me the step after eq#1.13? how eq#1.13 converted in the form of eq#1.14?

 

[wabbit]

The step from 1.13 to 1.14 is just $1-\frac{v^2}{c^2}=(1- \frac{v}{c})(1+ \frac{v}{ c})$

 

[applied ahmed]

The step from 1.13 to 1.14 is just $1-\frac{v^2}{c^2}=(1- \frac{v}{c})(1+ \frac{v}{ c})$

but how comes a square root in the denominator of eq#1.14

 

[applied ahmed]

thanks my problem solved