# The Doppler Effect of police car

## Homework Statement

There is a classic story (likely apocryphal) about an astronomer who was caught by a policeman for running a red light. The astronomer went to court and pleaded innocent, saying that the motion of his car made the red light (with a wavelength around 700 nm) shift to a green color (with a wavelength around 500 nm) due to the Doppler shift. The judge said something like “OK, you’re innocent of running a red light, but by your own testimony I am convicting you of speeding!” How fast would the astronomer have to have been speeding for his story to have been true? That is, calculate the velocity needed for the claimed color shift to be true. [express this velocity as a fraction of the speed of light.]

## Homework Equations

Given: (V_rad/c)=Δλ/λ_o

## The Attempt at a Solution

(500nm-700nm)/700nm=V_rad/(3x10^5km/s)
V_rad = -85714.29km/s
or
-.2857c

*********Am I doing my math correctly here? What is the significance of a negative value for V_rad? Do I just need to specify what direction I call positive and negative to eliminate the negative sign?

## Answers and Replies

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
You solved it correctly. The negative sign indicates a blue shift which means the car is approaching the light rather than moving away from it.

1 person
Okay I thought that may have been a possibility as well but thank you very much vela for clearing it up for me!