Basic problem regarding doppler effect of light (E/M waves)

[phys-lexic]

"Basic" problem regarding doppler effect of light (E/M waves)

1. At what speed would one have to move at to see a red light as green. Presume red light wavelength = 630nm and green light wavelength = 530nm.



2. f₀=f_s√(^[1+v/c]/_[1-v/c])
>f₀ = observed frequency
>f_s = source frequency
>v = velocity relative of source and observer
>c = speed of light (3.0e⁸)

The Attempt at a Solution

Our professor said we only need that equation to solve the proble, we were just introduced to the topic of light, relavitiy, and polarization (our chapter is on doppler effect). I assume that to get the answer you solve for v and plug the rest in, but that's been harder than i expected. Is there another formula i can use in combination with the one given or am i just not solving for v right...? thanks.

 

[quZz]

Square both sides and solve the linear equation for v

 

[phys-lexic]

i did that... would anyone mind checking my answer?

v=[(c)(^f₀/_fs)²-c] / [(^f₀/_fs)²+1]

and my final answer for v was 5.14 x 10⁷ m/s, towards the source because the wavelength shifts from the source, 630nm, to that observed, 530nm, a blue shift...?

 

[quZz]

I got v = 5.13 x 10⁷ m/s but that's a minor detail =) since the formula is the same

 

[phys-lexic]

sweet... thanks