Chapter 42: Problem 14

Question: With what speed would you have to go through a red light ( $\lambda~=~620~{\rm nm}$) in order to have it appear green ( $\lambda^\prime~=~540~{\rm nm}$)?

Solution: From the solution to Problem 42:13 (taking into account that we are moving toward the light), we have that

$${v\over c}~=~{ 1-\left({\lambda^\prime\over\lambda}\right)^2 \ove... ...left({\lambda^\prime\over\lambda}\right)^2 }~=~{1-0.87^2\over1+0.87^2}~=~0.138c$$