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How Do Police Radars Really Work?Problem:
Solution:
Since the photon energy, E, is equal to hn, where h = Planck's constant = 6.63 X 10^{-34} j sec, then Also, since photon momentum equals h/c, where c is the speed of light, then where the first term on the RHS represents p for an elastic reflection (i.e., one for which E = 0), and the second term takes into account the change in frequency due to the change in energy. Dividing eq. 1 by eq. 2, and substituting for E and p from eqs. 3 and 4, we find
This equation may be simplified to read
where the final step results from V << c. Now, let V = 60 mph = 27 m/sec, and let = 5 X 10^{8} Hz. Then,
The police radar detector easily detects this frequency shift. |
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