Question

The earth is moving towards a fixed star with a velocity of $30km{s}^{-1}$ . An observer on the earth observes a shift of $0.58A^0$ in the wavelength of light coming from the star. The actual wavelength of light emitted by the star is then

• A. $5800A^0$
• B. $2400A^0$
• C. $12000A^0$
• D. $6000A^0$

Answer 1

The correct option is A $5800A^0$

Given: The speed of the earth towards the star is $30km/s$.

The shift in the wavelength observed by the observer is $0.58A^o$

The actual wavelength of the light emitted by the star is given by:

$\Delta \lambda =\frac{v}{c}\left[\lambda \right]$

Here, $v=30km{s}^{-1}=30\times {10}^{3}m{s}^{-1}$

$c=3\times {10}^{8}m{s}^{-1},\Delta \lambda =0.58A^{\circ }$

$\lambda =\frac{c}{v}.\Delta \lambda =\left(\frac{3\times {10}^8}{30\times {10}^3}\right)\times 0.58$
$=5800A^o$