Question

You're caught running a red light on Hwy 316. Attempting to impress the skeptical patrol officer with your physics knowledge, you claim that you were traveling so fast that the red light (687 nm) appeared yellow (582 nm) to you.How fast would you have been traveling (in mi/hr) if that had been the case?
If you had been traveling that fast and the light actually was yellow, what color would it have seemed to you?

Answer 1

Answer

given,

wavelength of the red light,λ = 687 nm

wavelength of the yellow light = 582 nm

Frequency of red light

=$\dfrac{v}{\lambda}$

=$\dfrac{3\times 10^8}{687\times 10^{-9}}$

= 4.36 x 10¹⁴ Hz

frequency of the yellow light

=$\dfrac{3\times 10^8}{582\times 10^{-9}}$

= 5.15 x 10¹⁴ Hz

speed of the car

$f = f_o(\dfrac{c+v_r}{c})$

v_r is the required speed.

$5.15\times 10^{14}=4.36\times 10^{14}(\dfrac{c+v_r}{c})$

v_r = 0.19 c

v_r = 0.19 x 3 x 10⁸ =5.7 x 10⁷ m/s

1 m/s = 2.23694 mile/hr

v_r = 1.27 x 10⁸ mile/hr

if the light is actually yellow

f₀ = 5.15 x 10¹⁴ Hz

$f =5.15\times 10^{14}(\dfrac{c+0.19c}{c})$

f = 6.13 x 10¹⁴ Hz

wavelength corresponding to this frequency is wavelength = 493.2 nm

hence, the color corresponding to this wavelength is Green.