Answer to Question #164249 in Optics for Vanessam

Question

          

 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.λo from the car, to reach the car.

 (a Derive an expression for the wavelength λ of the radiation reflected from the car

(b) If Zo = 0 im, c = 3.0 × 108ms'1 and u = 33ms'1, calculate the change in wavelength of tho

    radiation received at the set after reflection from the car. 

Answer 1

Given quantities: $\lambda_o$ $c$ $u$

The beat frequency between a microwave transmitted signal and a reflected signal of a moving object is

$f_{reflected} - f_{transmitted} = \Delta f = \large\frac{2\nu_{target}}{c}f$

where the target velocity is taken as positive if the target if approaching the transmitter. Police RADAR uses this method for measurement of auto speed.

$\large\frac{\Delta f}{f} = \frac{2u}{c}$

$\large\frac{\lambda}{\lambda_0} = \frac{2u}{c} \to \lambda = \large\frac{2u}{c}\lambda_o$

2) $\large\frac{\lambda}{\lambda_0} = \frac{2u}{c} = \frac{2*33*10^{-3}}{3*10^8} =$ $22*10^{-11}$