Running Red Lights: How Fast Do You Have to Go?

[aChordate]

Homework Statement

A police officer pulls you over for running a red light. You tell the
officer, “But the light looked green to me!” How fast would you have to be traveling for
this statement to be true?

Homework Equations

?

The Attempt at a Solution

Can anyone point me in the right direction?

 

[Dick]

Homework Statement

A police officer pulls you over for running a red light. You tell the
officer, “But the light looked green to me!” How fast would you have to be traveling for
this statement to be true?

Homework Equations

?

The Attempt at a Solution

Can anyone point me in the right direction?

It's a doppler effect question. Look up the approximate wavelengths of red and green light and figure out how fast you would have to be traveling to shift one into the other. It won't be an exact number, since 'red' and 'green' aren't exact wavelengths.

 

[CWatters]

Table of colour vs frequency here..

http://en.wikipedia.org/wiki/Visible_spectrum

 

[aChordate]

λ_red=650nm=650*10^-9m
λ_green=510nm=510*10^-9m

f*λ=c c=2.99*10^8

f_o=f_s(1+/-v_rel/c)

f_o=5.863*10^14
f_s=4.6*10^14

5.863*10^14Hz=4.6*10^14Hz (1-v_rel/c)

v_rel=3.8%*10^8m/s

Is this correct?

 

[rude man]

Wrong formula. needs correction for relativistic effect.

I don't know what the % sign is doing in your answer, but if it shouldn't be there then you'd be going faster than the speed of light, which Al said is a no-no.

 

[PeterO]

Homework Statement

A police officer pulls you over for running a red light. You tell the
officer, “But the light looked green to me!” How fast would you have to be traveling for
this statement to be true?

Homework Equations

?

The Attempt at a Solution

Can anyone point me in the right direction?

My understanding is that "red-shift" occurs when the light source is moving away from you (relatively speaking), but the motorist is clearly moving towards the light.

 

[OmCheeto]

My understanding is that "red-shift" occurs when the light source is moving away from you (relatively speaking), but the motorist is clearly moving towards the light.

Quick! You still have time to delete your dyslexic post!

ps. I agreed with you at first, as I am totally dyslexic. But then I saw that Dick and CWatters had commented, and would have caught that in a second, so I double checked, and red light is the lower frequency, meaning lower energy. Ergo, going faster would shift the light to a higher frequency, and therefore to green.

 

[PeterO]

Quick! You still have time to delete your dyslexic post!

ps. I agreed with you at first, as I am totally dyslexic. But then I saw that Dick and CWatters had commented, and would have caught that in a second, so I double checked, and red light is the lower frequency, meaning lower energy. Ergo, going faster would shift the light to a higher frequency, and therefore to green.

Correct - damn it, I was trying to make the Green light appear Red !

 

[haruspex]

5.863*10^14Hz=4.6*10^14Hz (1-v_rel/c)

v_rel=3.8%*10^8m/s

Is this correct?

As rude man says, you'd do better using the relativistic formula: http://en.wikipedia.org/wiki/Relativistic_Doppler_effect.
But with the formula you used you should have been fairly close. I don't understand what you did after 5.863*10^14Hz=4.6*10^14Hz (1-v_rel/c). You should have got 27%*c. The relativistic version makes it a bit lower.