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34P

Expert-verifiedFound in: Page 1147

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of ${{\mathbf{\lambda}}}_{{\mathbf{o}}}{\mathbf{=}}{\mathbf{589}}{\mathbf{}}{\mathbf{nm}}$. Wavelength **${\mathbf{\lambda}}$** is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift ${\mathbf{\lambda}}{\mathbf{-}}{{\mathbf{\lambda}}}_{{\mathbf{o}}}$?**

The wavelength shift for sodium light source is 2.97 nm.

The proper wavelength of emitting light is ${\mathrm{\lambda}}_{\mathrm{o}}=589\mathrm{nm}$

The speed of sodium light source is $\mathrm{u}=0.1\mathrm{c}$

**The wavelength shift is the variation in the wavelength of light due to relative movement of source and observer in different frames. It is calculated by the wavelength shift formula.**

The wavelength shift for sodium light source is given as:

$\mathrm{\lambda}-{\mathrm{\lambda}}_{\mathrm{o}}={\mathrm{\lambda}}_{\mathrm{o}}\left(\frac{1}{\sqrt{1-{\left(\frac{\mathrm{v}}{\mathrm{c}}\right)}^{2}}}-1\right)$

Substitute all the values in the above equation.

$\mathrm{\lambda}-{\mathrm{\lambda}}_{\mathrm{o}}=\left(589\mathrm{nm}\right)\left(\frac{1}{\sqrt{1-{\left(\frac{0.1\mathrm{c}}{\mathrm{c}}\right)}^{2}}}-1\right)\phantom{\rule{0ex}{0ex}}\mathrm{\lambda}-{\mathrm{\lambda}}_{\mathrm{o}}=2.97\mathrm{nm}$

Therefore, the wavelength shift for sodium light source is 2.97 nm.

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