Suppose a rocketship is receding from the earth at a speed of 2/10 th 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?

Options

A. Blue
B. Orange
C. Yellow
D. Yellow-orange

Answer

D

Explanation

The observer on the earth will detect a wavelength given by
`v=pm (lambda-lambda_0)/lambdac`
where `lambda`=original wavelength
`lambda_0` = apparent wavelength
v=velocity of source
Here, source is receding, therefore +ve sign will be taken
`because 2/10 c = (lambda-lambda_0)/lambda c`
`rArr (lambda-lambda_0)/lambda=2/10 rArr 1-lambda_0/lambda=2/10`
`rArr lambda_0/lambda=1-2/10 =8/10 rArr lambda=10/8 lambda_0 = 1.25 lambda_0`
The wavelength of blue light varies from 450 nm to 475 nm. Therefore, the observed light will have wavelength ranging from 562.5 nm to 593.75 nm which will be yellow orange.