# Writing down algebraic expression

1. Jan 22, 2009

### thundercats

1. The problem statement, all variables and given/known data
An object emitting light with a wavelength of L is traveling away from you with a relative speed of v, which is small compared to the speed of light. Write down the algebraic expression for the fractional change in wavelength between what you observe and what the object emits. (In other words, you're trying to find Delta L/L

2. Relevant equations
F'=F(1-(U/C)) minus sign because its moving away
F=C/L L= lambda :D

3. The attempt at a solution
i just cant seem to be able to rearrange the equation to a point i have
change in wavelenght/wave lenght
i mean i know L of source/L observed= 1- U/C where u is relative speed while c is the speed of light i cant seem to get any further. i would appreciate it if someone is able to show me how to rearrange this equation

2. Jan 22, 2009

### Hootenanny

Staff Emeritus
HINT:

$$f^\prime = f\left(1-\frac{u}{c}\right)$$

\begin{align*}\Rightarrow f^\prime - f & = f\left(1-\frac{u}{c}\right) - f = f\left(1-\frac{u}{c}-1\right)\\ & = - f\frac{u}{c}\end{align*}

3. Jan 22, 2009

### thundercats

so does that mean that delta L/L= C/v. and since v is smaller than the speed of light would the answer be delta L (L is lambda)/L=C

4. Jan 22, 2009

### Hootenanny

Staff Emeritus
That would be correct.
No. I think that what the question meant was that we could use the classical Doppler shift (as we did) rather than the relativistic one.

Note that if v << C then (C/v) >> C.

5. Feb 9, 2009

### thundercats

thnx by the way