Question

Police check your speed using a light source that operates at 900 nm. You are in...

Police check your speed using a light source that operates at 900 nm. You are in a car driving towards the officer at 78 mph. What is the wavelength and frequency of the light that is reflected from your car that the officer detects?

The wavelength of the reflected light is ____nm.

The frequency of the reflected light is ___Hz.

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Answer #1

Given the wavelength of light source = 900nm = 900 x 10-9m. If c is the velocity of light (c = 3 x 108m/s), the frequency of light source is

The listener (car) is approaching towards the source at a speed of v = 78mph = 34.87 m/s.

Taking the source to be at rest, the apparent frequency of light recieved by the car is given by

This is the frequency recieved by the car. Now this frequency is reflected back to the officer. Now the apparent frequency recieved by the officer is,

Here the apparent frequency and the source frequency are same. So the wavelength of the reflected light is 900nm.

Also the frequency of the reflected light is 3.33 x 1014Hz.

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