Optics Question 235

Question: The observed wavelength of light coming from a distant galaxy is found to be increased by 0.5% as compared with that coming from a terrestrial source. The galaxy is

[MP PMT 1993, 2003]

Options:

A) Stationary with respect to the earth

B) Approaching the earth with velocity of light

C) Receding from the earth with the velocity of light

D) Receding from the earth with a velocity equal to $ 1.5\times 10^{6}m/s $

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Answer:

Correct Answer: D

Solution:

$ \frac{\Delta \lambda }{\lambda }=\frac{v}{c}, $ Now $ \Delta \lambda =\frac{0.5}{100}\lambda \Rightarrow \frac{\Delta \lambda }{\lambda }=\frac{0.5}{100} $

$ \therefore v=\frac{0.5}{100}\times c=\frac{0.5}{100}\times 3\times 10^{8}=1.5\times 10^{6}m/s $ Increase in l indicates that the star is receding.



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