The speed with which one has to drive to see a red light as green.
Answer to Problem 57P
The speed with which one has to drive to see a red light as green is
Explanation of Solution
To occur a Doppler shift of magnitude in which a red light is seen as green, a relativistic relative velocity is required.
The observer is approaching the source and the source of light is stationary in this case. This implies the relative velocity is greater than zero.
Here,
Write the equation for the Doppler effect of EM waves.
Here,
Divide both sides of the above equation by
Rearrange the above equation.
Rewrite the above equation for
Since frequency of the EM waves is inversely proportional to their wavelength, write .expression for
Here,
Put the above equation in equation (I).
Conclusion:
Given that the wavelength of red is
Substitute
Therefore, the speed with which one has to drive to see a red light as green is
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