How fast would you have to drive in order to see a red light as green? Assume $\lambda=630 \mathrm{~nm}$ for red and $\lambda=$ $530 \mathrm{~nm}$ for green.
A) $5 \times 10^{7} \mathrm{~m} / \mathrm{s}$
B) $5 \times 105 \mathrm{~m} / \mathrm{s}$
C) $5 \times 106 \mathrm{~m} / \mathrm{s}$
D) $5 \times 104 \mathrm{~m} / \mathrm{s}$

Question

Quizplus · Accepted Answer

To see a red light ($\lambda = 630 \, \text{nm}$) as green ($\lambda = 530 \, \text{nm}$), we can use the Doppler effect formula for light: $\lambda' = \lambda \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}$, where $\lambda'$ is the observed wavelength, $\lambda$ is the emitted wavelength, $v$ is the velocity of the observer relative to the source, and $c$ is the speed of light in vacuum ($3 \times 10^8 \, \text{m/s}$). Solving for $v$ when $\lambda' = 530 \, \text{nm}$ and $\lambda = 630 \, \text{nm}$, we find that $v$ is approximately $5 \times 10^7 \, \text{m/s}$.

How Fast Would You Have to Drive in Order to See