Chapter 38, Problem 11P

A light source recedes from an observer with a speed ν_s that is small compared with c. (a) Show that the fractional shift in the measured wavelength is given by the approximate expression

$\frac{\Delta \lambda }{\lambda }=\frac{v_S}{c}$

This phenomenon is known as the redshift because the visible light is shifted toward the red. (b) Spectroscopic measurements of light at λ = 397 nm coming from a galaxy in Ursa Major reveal a redshift of 20.0 nm. What is the recessional speed of the galaxy?