Question

A light source approaches the observer with a velocity $0.8C$. The Doppler shift for light of wavelength $5000\mathring{A}$ is ____

• A. $4400\mathring{A}$
• B. $1833\mathring{A}$
• C. $3167\mathring{A}$
• D. $7333\mathring{A}$

Answer 1

The correct option is C $3167\mathring{A}$

According to Doppler's principle ${\lambda }^{\prime }=\lambda \sqrt{\frac{1-v/c}{1+v/c}}$ for $v=c$
${\lambda }^{\prime }=5500\sqrt{\frac{(1-0.8)}{1+0.8}}=1833.3$
$\therefore$ Shift $=5500-1833.3=3167\stackrel{o}{A}$