Wikipedia:Reference desk/Archives/Mathematics/2015 June 5

= June 5 =

How close is the answer to correct?
Hi, I was wondering if anyone could let me know if my solution to this homework problem is close to correct or if I am way off base?

"How fast must a car be going in order for the driver to perceive a red light as a green light? Assume red light = 700 nm and green light = 500 nm"

I wrote:

To solve this we will use the formula:

v / c = (λ shifted - λ unshifted) / (λ unshifted)

v = c (λ shifted - λ unshifted) / (λ unshifted)

v = c ( 500 - 700 ) / 700

v = c (-2/7)

v = (3 * 10 ^ 8)m/s * -2/7

v = -86 * 10 ^ 6 m/s

In order to see the red light as green, the driver would have to be speeding away from the light at .86 million kilometers an hour.

Am I close? Thanks!!!

Duomillia (talk) 20:18, 5 June 2015 (UTC)


 * Relevant articles: Doppler effect and particularly Redshift. Which direction causes redshift, which direction causes blueshift, and which of the two is being experienced in this problem? -- ToE 20:57, 5 June 2015 (UTC)
 * Also check your conversion between m/s and km/hr; how are you doing that? Finally, note that you are using a non-relativistic formula, which is good for velocities which are small with respect to c.  You may be interested in trying the relativistic formula as given in Redshift (for motion completely in the radial direction) and comparing that to your non-relativistic result. -- ToE 21:16, 5 June 2015 (UTC)