Question

A source of light emitting wavelength $\lambda =600nm$ is moving away from the observer at a speed close to 1/5th the speed of light in vacuum. When observed, what will be wavelength percieved for the source?

• A. 490 nm
  
• B. 735 nm
  
• C. 684 nm
  
• D. 637 nm
  

Answer 1

The correct option is B 735 nm

As the source of light is moving away at velocity $v=e/5$, the observed wavelength would be re-shifted $({\lambda }^{\prime }>\lambda )$

From Doppler's formula

${\lambda }^{\prime }=\lambda \sqrt{\frac{c+v}{c-v}}$ we have :

$=\lambda \sqrt{\frac{c+c/5}{c-c/5}}=\lambda \sqrt{\frac{6/5c}{4/5c}}=\lambda \sqrt{\frac{3}{2}}$

Putting $\lambda =600nm,$ we get :

${\lambda }^{\prime }=600\sqrt{\frac{3}{2}}=734.85mn$