A physics professor claims in court that the reason he went through the red light (wavelength = 650 nm) was that, due to his motion, the red color was Doppler shifted to green (wavelength = 550 nm). How fast was he going?Carrying out the calculation using the formula (f' = observed frequency, f = original frequency, v = speed the professor was going, c = speed of light (around 3 x 108 m/s),
f' = f [(1+v/c)/(1-v/c)]1/2If he managed to drive at that speed, he will get away from both the red light ticket and the speeding ticket since people will be more interested in finding out what car he was driving :)
c/550nm = c/650nm x [(1+v/c)/(1-v/c)]1/2
...blah blah blah...
v = 4.96(107) m/s = 110 million miles/hour
(To people in education: See the power of a little humor! Even after 10 years I can still kind of remember what Doppler effect is. Try to make the textbooks/lectures more fun and students will remember a lot more about what they learn!)