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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)[reply]

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)[reply]

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#Redshift formulae (for motion completely in the radial direction) and comparing that to your non-relativistic result. -- ToE 21:16, 5 June 2015 (UTC)[reply]