Optics Question 254

Question: In the spectrum of light of a luminous heavenly body the wavelength of a spectral line is measured to be 4747 Å while actual wavelength of the line is 4700 Å. The relative velocity of the heavenly body with respect to earth will be (velocity of light is $ 3\times 10^{8}m/s $ )

[MP PMT/PET 1998]

Options:

A) $ 3\times 10^{5}m/s $ moving towards the earth

B) $ 3\times 10^{5}m/s $ moving away from the earth

C) $ 3\times 10^{6}m/s $ moving towards the earth

D) $ 3\times 10^{6}m/s $ moving away from the earth

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Answer:

Correct Answer: D

Solution:

$ \Delta \lambda =\frac{v _{s}}{c}\lambda \Rightarrow v _{s}=\frac{\Delta \lambda .c}{\lambda }=\frac{47\times 3\times 10^{8}}{4700} $

$ =3\times 10^{6}m/s $ away from earth



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