All Problems

Optics of Moving Sources

Problem 5.233

How fast should a car move for the driver to perceive a red traffic light \((\lambda \approx 0.70 \mu \mathrm{m})\) as a green one \(\left(\lambda^{\prime} \approx 0.55 \mu \mathrm{m}\right) ?\)

Reveal Answer
v=c(λ/λ)21(λ/λ)2+1=7.1104 km/sv=c \frac{\left(\lambda / \lambda^{\prime}\right)^{2}-1}{\left(\lambda / \lambda^{\prime}\right)^{2}+1}=7.1 \cdot 10^{4} \mathrm{~km} / \mathrm{s}