Question

You have just been pulled over for running a red light. In an attempt to get out of the resulting traffic fine, you tell the police officer that as you drove toward the traffic signal the red light was Doppler shifted so much that it appeared green to you. “Ok,” says the officer, “then I’ll ticket you for speeding. The fine is $1 for every 1km/h over the posted speed limit of 50 km/h.” How big is your fine? Use 650 nm as the wavelength of red light and 540 nm as the wavelength of green light. Hint: Remember that nothing can go faster than the speed of light.

Answer 1

when there is a relative motion between the source and the observer, then the frequency of light appears to be shifted by either highte or lower frequencey than the original frequency emitted by the source.

When the observer is moving towards the source with a velocity , then the apperant frequency is releated to the frequency emitted by the source as :

putting in the values,

The frequency and wavelength of light is releated by

Where is frequency and is wavelength.

=frequency of green light =

=frequency of red light =

the overspeed is (approximately)

Hence net fine for over speeding is