# How fast would you have to go to claim you saw the red light as green due to the Doppler Effect?

Driving toward it, I suspect you would have to be going at relativistic speeds.

Calculating this, it appears to be around 1/6 the speed of light when driving directly at it, but since you are on the road and it is in the air, I can't calculate the angle well.

This could make for a good excuse to the cops :)

• What have you done to try to figure this out yourself? Apr 23 '15 at 13:12
• See edit. @David Z Apr 23 '15 at 13:14
• The angle is not an issue, since you would be thousands of miles away. And you would most certainly have to admit to exceeding the speed limit. Apr 23 '15 at 13:33
• I remember this was a practice problem in my Physics class in HS. The answer was "I'm not giving you a ticket because you passed a red traffic light, but man that speeding ticket will be something!" Apr 23 '15 at 14:18
• @ writing thesis plus all the destruction :P Apr 23 '15 at 21:16

Let me (try) to quote:

How fast would you have to go in your car to run a red light claiming that it appeared green to you due to the Doppler Effect? —Yitzi Turniansky

As expected, quoting and mathjaxing are two things that do not go together well, the rest of this post should be considered a quote:

$$\frac{Red ~light~ wavelength}{Green~ light~ wavelength}=\sqrt{\frac{1+\frac{Your ~speed}{Speed~ of~ light}}{1−\frac{Car~ speed}{Speed~ of~ light}}}$$

$$Car speed=\frac{c×(Red ~light~ wavelength²−Green~ light~ wavelength²)}{Green~ light~ wavelength²+Red~ light~ wavelength²}≈\frac16c$$

Solely for your amusement I'd like to point out how happy I felt when finally getting this formula right and how quickly that feeling diminished when I realized I could have simply copy & pasted the mathjax code from the page source. duuuh

• @zeldredge I deleted the comment since the answer was edited Apr 23 '15 at 14:33