The apparent wavelength of the light from a star moving away from the earth is 0.2% more than its actual wavelength. Then the velocity of the star is(a) 6 × 10⁷ m/sec(b) 6 × 10⁶ m/sec(c) 6 × 10⁵ m/sec(d) 6 × 10⁴ m/sec
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the true answer is b
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Apparent wavelegth = 0.2% ( Given)
The apparent frequency for a light source moving away with velocity U will be given as -
V = c/c+u.v0 a= c/λ
Thus λ° = c+u/v0
Δλ = λ°-λ = u/v0 = u/cλ0
= Δλ/λ°×100%
= u/c×100
= 0.2 = u/c×100
= u = 3× 10 to the power 8 × 0.2/100
= 6 × 10⁵ m/sec
Thus the velocity of the star is = 6 × 10⁵ m/sec
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