# Special Relativity Problem

1. Apr 14, 2010

### iaberrant

By now i must be driving you guys crazy with my relativity questions , but this is my last one! i swear! =]

1. The problem statement, all variables and given/known data

A noted physicist was stopped by police for travelling through a red traffic light. The physicist argued that to because he was travelling fast, the colour of the light had changed from the red wavelength to that of a green wavelength

The judge said that he would let him off the charge of running the red light, but would fine him for speeding at the rate of one cent for every 100km/hr he was travelling over 100km/hr

Was he fined? and how much was his fine?

Assume
c=3x10^8ms-1
frequency of red light=4.5x10^14 Hz
frequency of green light= 6.0 x 10^14 Hz

2. Relevant equations

Would this problem also be related to the Dopper Shifty as the change of colour of the traffic lights? And therefore would the doppler shift be appropriate to use in this case ? But i have come across a relativistic doppler formula; f/f0 = √[(1 + v/c)/(1 - v/c)] ?

there is a non relativistic doppler formula ?
hence ;
∆f = f0*(v/c)

v = ∆f/f0 * c

where ;
∆f = 1.5*10^14
f0 = 4.5*10^14
v = 0.33 c

How can i go about this problem and any other ideas of what is involved in solving the problem ?