Q56P - University Physics with Modern Physics

Question

In a laboratory, light from a particular spectrum line of helium passes through a diffraction grating and the second-order maximum is at 18.9° from the center of the central bright fringe. The same grating is then used for light from a distant galaxy that is moving away from the earth with a speed of $\mathbf{2}\mathbf{.}\mathbf{65}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathit{m}\mathbf{/}\mathit{s}$. For the light from the galaxy, what is the angular location of the second-order maximum for the same spectral line as was observed in the lab?

Step-by-Step Solution

Answer

The angular location of the second-order maximum for the same spectral line as was observed in the lab is $20.7°$ and this is the angular location of the galaxy's second-order maximum for light.

Step 1: Doppler Effect

Step 2: The angular location of the second-order maximum for the same spectral line as was observed in the lab

The equations for the same spectral lines seen in the lab as well as in the galaxy;

By dividing;

Using the relationship , the equation  is;

By substituting;

Hence, the angular location of the second-order maximum for the same spectral line as was observed in the lab is $20.7°$ and this is the angular location of the galaxy's second-order maximum for light.