Light of a particular wavelength λs is emitted from the Sun. At any instant, a band of wavelengths ranging from less than λs to more than λs is observed on the Earth.

Question 5

Light of a particular wavelength λs is emitted from the Sun. At any instant, a band of wavelengths ranging from less than λs to more than λs is observed on the Earth. This is caused by the Doppler effect.

 

What could be the explanation for this Doppler effect?

A The Sun is moving at right-angles to a line joining the Sun and the Earth.

B The Sun is moving away from the Earth.

C The Sun is moving towards the Earth.

D The Sun is rotating.

Reference: Past Exam Paper – November 2017 Paper 11 Q25

Solution:

Answer: D.

In the Doppler effect, the observed frequency / wavelength changes due to the motion of either the source or the observer, or both.

Here, the source is the Sun and the observer is on the Earth.

A shorter wavelength is observed when the source approaches the observer. [case C]

A longer wavelength is observed when the source moves away from the observer. [case B]

In this case, we are told that at ANY instant, a band of wavelengths ranging from less than to more than the wavelength λ_s of the light is observed. That is, at any time, both longer and shorter wavelengths are observed. This cannot correspond to only case B nor only case C. [B and C are incorrect]

If the Sun is moving at right-angles to a line joining the Sun and the Earth, we may observed both longer and shorter wavelength as at some point, the Sun would be approaching the Earth and at some other time, it would be receding. However, this will occur one at a time. The observed wavelength will be either always be shorter until it reaches the line joining the Sun and Earth and afterwards, it becomes longer and continues to be longer. And vice versa. [A is incorrect]

 

Now, consider the case where the Sun is rotating. If the rotation is such that the east end of the Sun is approaching the Earth (this would result in a shorter observed wavelength), the west end of the Sun would be moving away from the Earth (thus longer wavelength are observed). This occurs at the same instant. So, we have a range of wavelengths both shorter and longer than the wavelength of the source.