# Why didn't I experience violet shift at traffic signals?

context: we were studying sound waves and our instructor informed us about doppler effect and violet shift of light. Now I have many times exceeded the speed limit at night where there were no cameras and choose to ignore traffic signal when it was in red color, I never observed the red color to turn into violet, or blue or green
Why didn't I see any other color with lower frequency other than red?, Is there any speed thershold that has to be satisfied in order to experience violet shift?

• Calculate what your speed was as a fraction of c, and therefore how much you would expect a 650 nm red light to be shifted. Is it violet, blue, or green? Commented Nov 11, 2021 at 4:48
• Then you can calculate how fast you need to run a red light for it to appear green. Commented Nov 11, 2021 at 8:13

The following equation $$\lambda_o=\lambda_s\ \sqrt{\frac{1+\beta}{1-\beta}}$$ is used to calculate the relative motion Doppler shifted wavelength of light, and $$\beta=\frac{v}{c}$$ where $$v$$ is the relative velocity of the source and observer and $$c$$ is the speed of light.

If we consider a car moving at a speed of $$100$$ miles per hour, the magnitude of this term becomes $$\beta\approx \frac{44}{3\times 10^8}\approx 1.5\times 10^{-7}$$ meaning $$\lambda_o\approx\lambda_s$$ so that the Doppler shift in the color will be unnoticeable.

To see red light $$650\ nm$$ shifted to violet light $$380\ nm$$, then using the above equation, you would have to approach the red light at a speed of $$\approx 1.3\times 10^8 \ ms^{-1}$$ or $$289,500,000$$ miles per hour, which is a little fast.

PS Don't speed or run through red lights.

• 380 nm is quite extreme violet, I'd say it's UV already. Commented Nov 11, 2021 at 22:50

This one of the situations where special relativity comes in. Now formula for longitudnal doppler effect is: $$\nu=\nu_0\sqrt{\frac{1+v/c}{1-v/c}}$$, where: $$\nu$$ is obserevd frequency of light, $$\nu_0$$ is original frequency of light, $$v$$ is relative velocity between source and observer (taken as $$+$$ for approach, and $$-$$ for recced) and $$c$$ is speed of light.

Note that in our daily life speeds are way lesser in comparision to $$c$$, so $$v/c\approx0$$, and $$\nu=\nu_0$$, so we don't experience this effect in real life. You can calculate speed required for red to turn violet by above formula, which would probably be orders of magnitude beyond our currently capabilities.