Doppler Effect

This is not 93 physics MC...

題意：在實驗室內，一氫氣源頭放射一線光譜，有一線在波長656.3 nm。若有一恆星以速率200 kms^-1遠離地球，那麼在地球上觀察那星所放射的線會是哪個波長？


The answer is C. 656.7 nm.

Note that this is concerning the EM wave, therefore relativistic Doppler Effect has to be considered. And light has the absolute speed c.

As the two objects are separating,

f' = f√[(c - u) / (c + u)]

c/λ' = c/λ √[(c - u) / (c + u)]

λ' = λ√[(c + u) / (c - u)]

Putting λ = 656.3 X 10^-9 m

c = 3 X 10^8 ms^-1

u = 200 X 10^3 ms^-1

You will get answer C.