Question

A STAR EMITTING RADIATION AT A WAVELENGTH OF 5000Å IS APPROACHING EARTH AT A VELOCITY OF 1.5x10^6 m/s. THE CHANGE IN WAVELENGTH ON EARTH IS :
1. 2.5Å
2. 1000 Å
3. ZERO
4. 25 Å

Answer 1

Answer on Question #40568 - Physics - Optics

Question: A STAR EMITTING RADIATION AT A WAVELENGTH OF 5000A IS AP- PROACHING EARTH AT A VELOCITY OF $1.5\times 10^{6}$ m/s. THE CHANGE IN WAVELENGTH ON EARTH IS : 2.5A, 1000A, ZERO or 25A Solution. The formula for relativistic Doppler effect is

$\lambda_{o}=\sqrt{\frac{1+\beta}{1-\beta}}\lambda_{s}$

where $\lambda_{o}$ is observed wavelength, $\lambda_{s}$ is emitted wavelength and $\beta=v/c$ where $c$ is speed of light and $v=1.5\cdot 10^{6}$ m/s. So, we have

$\delta\lambda=\lambda_{o}-\lambda_{s}=\lambda_{s}(1-\sqrt{\frac{1+\beta}{1-\beta}})=\lambda(1-\sqrt{\frac{1+1.5\cdot 10^{6}/3\cdot 10^{8}}{1-1.5\cdot 10^{6}/3\cdot 10^{8}}})\approx 25\,\AA$

Answer is $25$ $\AA$.