Question

You have just been pulled over for running a red light. The officer informs you that the fine will be $250. You argue that the laws of physics prevented you from observing that the light was red (~650 nm), since it was Doppler-shifted to where it appeared green (~540 nm) to you. “OK” says the officer (who moonlights as a physics professor), “then I will fine you for speeding”. The fine is $1 for every km/h over the posted 50 km/h. How big is your fine?

Answer 1

The relation for doppler shift is

Where

is wavelength shift,

is wavelength of stationary source,

is speed of observer and

is speed of light.

Putting the given values in the relation

So, the fine is