A cautionary tale: A physicist is in court, defending herself on the charge of r

Question

A cautionary tale: A physicist is in court, defending herself on the charge of running a red light. She testifies that because of the Doppler effect, as she approached the intersection the relatively low-frequency red light was shifted to higher-frequency green light, from her point of view. The judge fined her instead for speeding, 1 dollar for ever meter/second she was driving over the speed limit of 10m/s (36km/hr). How large was the fine? (The wavelength of red light is about 700nm, and the wavelength of green light is about 550nm) How much would the fine have been if the speed limit had been 20m/s?

Explanation / Answer

wavelength of red light is about = = 700nm, thus,fruqency of the red light : n = c /                                                                            = 3 x108/ 7x10-7                                                    = 0.428x1015 Hz    lly , for green light :    n ' = c/' = 3x108 / 5.50x10-7                                                                             = 0.545x1015 Hz                                                                             = 0.545x1015 Hz     Here , V = speed limit had been 20m/s                 Vr = 10 m/s                 Vs = ?                   It is known bythe formula for apparent frquency of light        n' = (20 + 10 / 20 + Vs ) n       0.545x1015    = (30/ 20 + Vs ) 0.428x1015           1.273     = 30 / 20 + Vs                20 + Vs = 23.56                         Vs = 23.56 - 20 = 3.56 m/s            but ,  judge fined her instead for speeding, 1 dollar for             ever meter/second                Hence ,  fine   was : 3.56 dollars

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