Answer to Question #164245 in Optics for Bella

Question

 What is Doppler Effect?

       A police radar set emits a parallel beam of electromagnetic radiation at wavelength λo and velocity c, Which falls on a motor car moving directly towards the set with a velocity u.

       (a.) Derive an expression for the time it takes for the wave front of the radiation initially a distance

       λo from the car, to reach the car.

Answer 1

The Doppler effect (or the Doppler shift) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

$f_r=f_t(\frac{1+v/c}{1-v/c}) \\ f_r=f_t(\frac{c+v}{c-v}) \\f_d=f_r-f_t=2v\frac{f_t}{c-v} \\f_d\approx 2v\frac{f_t}{c}$

$v=\frac{\lambda_0}{t} \\f_d\approx 2v\frac{f_t}{c}\approx 2\frac{\lambda_0f_t}{tc} \\t\approx 2\frac{\lambda_0f_t}{cf_d}$