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

AI Thread Summary
To see red light (630nm) as green light (530nm), one must move at a speed of approximately 5.14 x 10^7 m/s towards the light source, resulting in a blue shift. The relevant formula used is f0 = fs√([1+v/c]/[1-v/c]), where f0 is the observed frequency, fs is the source frequency, v is the relative velocity, and c is the speed of light. The user attempted to solve for v and confirmed their calculations yielded a speed consistent with the expected blue shift. The minor discrepancy in the final answer (5.14 vs. 5.13) was acknowledged as negligible. The discussion highlights the application of the Doppler effect in light, emphasizing the relationship between speed and wavelength shift.
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"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=fs√([1+v/c]/[1-v/c])
>f0 = observed frequency
>fs = 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.
 
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Square both sides and solve the linear equation for v
 


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...?
 


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


sweet... thanks
 

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