Suppose a rocketship is receding from the earth at a speed of 2/10th the velocity of light. A light in the rocketship appears blue to the passengers on the ship. What colour would it appear to an observer on the earth?

Light from a source moving away is redshifted (wavelength stretched), so radiation that is blue in the ship’s rest frame will be observed at longer wavelengths by an Earth observer [1]. For a recession speed β = 0.2, the relativistic longitudinal Doppler factor for wavelength is √((1+β)/(1−β)) ≈ √(1.5) ≈ 1.225, i.e., wavelengths increase by about 22.5%. Taking a typical blue wavelength (~450 nm) gives λ_obs ≈ 450×1.225 ≈ 551 nm, which lies in the yellow (yellow–green) part of the visible spectrum. Thus the Earth observer would see the light shifted from blue to yellow [2].

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 1: The Universe, The Big Bang Theory, Galaxies & Stellar Evolution > Doppler-Shift or Redshift and Blueshift > p. 3
2. [2] http://lifeng.lamost.org/courses/astrotoday/CHAISSON/AT303/HTML/AT30305.HTM