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?
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4$\begingroup$ 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? $\endgroup$– The PhotonCommented Nov 11, 2021 at 4:48
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$\begingroup$ Then you can calculate how fast you need to run a red light for it to appear green. $\endgroup$– Bill WattsCommented Nov 11, 2021 at 8:13
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2 Answers
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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.
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$\begingroup$ 380 nm is quite extreme violet, I'd say it's UV already. $\endgroup$– RuslanCommented Nov 11, 2021 at 22:50
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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.
