How Does Relativistic Speed Affect Photon Wavelength Measurement?

[ivykink]

Homework Statement

Spaceship Enterprise fires a photon torpedo at an approaching Klingon ship that has just decloaked. If the wavelength of this light beam as measured on the Enterprise is 616 nm what is the wavelength (in nm) as measured by the Klingon ship if the relative speed between the two space ships is u/c = 0.71?

Homework Equations

As far as I am concerned I have been working with L=L_o√1-u²/c²

The Attempt at a Solution

I am a little confused with the question as I am not exactly sure what is happening, this is what I have been doing L=616nm√1-.71² to get 433.8nm as the observed wavelength of the photon.

Now I am kinda confused with regard to the launching of the photon. It is my understanding that if it is a photon it would be moving at the speed of light toward the klingon ship? I am a little lost with how to approach the problem.
the answer is apparently 254nm.

Thank you for your assistance.

 

[Janus]

You should be thinking in terms of Doppler shift rather than length contraction.

(On a side note, what are they teaching in schools these days? Everyone knows that a Photon torpedo is not made of photons, but is a casing containing an antimatter charge and propelled by a small warp engine.)

 

[ivykink]

Thank you Janis :-) I had a feeling is was using the wrong relativity equations.

ps I think they are waiting for us to understand the foundation physics before introducing us to antimatter weapons and light speed travel ;-)