Question

6. A blue (473 nm) light source is moving at a relativistic speed v away from an observer.
a) Determine how fast the source would have to be moving (relative to the speed of light c) in
order for the observer to perceive red (650 nm) light.
b) How fast would it have to be moving for the observer to perceive green (500 nm) light?
c) If source is moving away at v = 0.5c, what wavelength will the observer measure?

Answer 1

Solved equations needed
a)\[v=(\lambda^2-\lambda_0^2)/(\lambda^2+\lambda_0^2)\]

Answer 2

b) same as a

Answer 3

c) \[\lambda=\lambda_0(\sqrt{(1+\beta)/(1-\beta)})\]

Answer 4

This is a plug and chug.

a) \[\lambda_{0}=473nm\]
\[\lambda=650nm\]
\[ \beta =(λ^2−λ_{0}^2)/(λ^2+λ_{0}^2)\]
\[ \beta =(650^2−473^2)/(650^2+473^2)\]

b) Exactly the same just use the different wavelength

c)
\[ \beta=v/c\]
and \[ \beta=0.5\]
\[λ=λ_{0}\sqrt{(1+β)/(1−β)}\]
\[λ=473\sqrt{(1+0.5)/(1−0.5)}\]

Answer 5

thanks, yeah I figured it out by plug and chug, I was just leaving the equations for others.