How fast would you need to travel to see a red light as green?

[cragar]

I remember reading in a book that if we approached a red light
really fast it would appear green to us due to the Doppler effect of light
does anyone know how fast we would need to travel for this to happen.

 

[jeffreydk]

If you are approaching a light source, then you can compute the shift in frequency of light by

$$\nu_O=\nu_S\sqrt{\frac{1-v/c}{1+v/c}}$$

where $\nu_O$ is the frequency seen by the observer, $\nu_S$ is the frequency emitted by the source of the light, c is the speed of light, and v is the speed that you're traveling toward the source.

 

[cragar]

sweet that helps , thank-you

 

[jeffreydk]

glad to help.

 

[v2kkim]

The equation above seems to have a typo, because the equation says when source approaches the observer the freq decreases , which is wrong.

 

[jeffreydk]

Ah yes there is a typo--for approaching the signs should be reversed

$$\nu_O=\nu_S\sqrt{\frac{1+v/c}{1-v/c}}$$