Question

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

• A. Blue
• B. Orange
• C. Yellow
• D. Indigo

Answer 1

The correct option is D. Yellow-orange.

The observer on the earth will detect a wavelength given by

$\nu =\pm \left(\frac{\lambda -{\lambda }_0}{\lambda }\right)c$

where λ = original wavelength

${\lambda }_0$ = apparent wavelength

ν = velocity of source

Here, source is receding, therefore +ve sign will be taken

=> $\frac{2}{10}c=\frac{\lambda -{\lambda }_0}{\lambda }c$

=> $\frac{\lambda -{\lambda }_0}{\lambda }=2/10$

=> $1-\frac{{\lambda }_0}{\lambda }=\frac{2}{10}$

=> $\frac{{\lambda }_0}{\lambda }=1-\frac{2}{10}=\frac{8}{10}$

=> $\lambda =\frac{10}{8}{\lambda }_0$

$\lambda =1.25{\lambda }_0$

The wavelength of blue light varies from 450 nm to 475 nm. Therefore, the observed light will have a wavelength ranging from 562.5 nm to 593.75 nm which will be yellow-orange.