The Doppler Effect for Light Waves

[sameejane]

Homework Statement

You are cruising to Jupiter at the posted speed limit of 0.1c when suddenly a daredevil passes you, going in the same direction, at 0.3c. At what wavelength does your rocket cruiser's light detecter "see" his red tail lights? Is this wavelength ultraviolet, visible, or infrared? Use 650 nm for the wavelength of red light.

Homework Equations

I used the dropper effect for the light of a receding source"
√((1+v_s/c)/(1-v_s/c) * λ_o

The Attempt at a Solution

I tried using 0.3c for the speed of the source, and 650 for λ_o. (I know the answer is 800 nm); I then tried using 0.1c instead. I got (almost) the right answer though when I plug in 0.2c... the wavelength came up as 796 nm.

Don't know what else to use!

 

[JesseC]

You need to think about relativistic velocity transformations:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/veltran.html

To simply add and subtract velocities as you would at non-relativistic speeds is not valid when you're traveling at a significant fraction of c.

 

[rude man]

Remember that the two cited speeds (and they should have been! ) are both with reference to Jupiter. It's not that you are observing the speeder going by you at 0.2c. Each has his own speedometer and those readings are 0.1c and 0.3c.

You need two formulas. One to give you the true relative speed between the two rocket ships and the other to compute the Doppler shift relativistically.


BTW I got 801.2368685 nm.