Writing down algebraic expression

[thundercats]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

i just can't 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 can't seem to get any further. i would appreciate it if someone is able to show me how to rearrange this equation

 

[Hootenanny]

HINT:

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

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

 

[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

 

[Hootenanny]

so does that mean that delta L/L= C/v.

That would be correct.

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

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.

 

[thundercats]

thnx by the way