I have D lines at 589.0 nm and 589.6 nm. A diffraction grating with 531.5 lines...

I have D lines at 589.0 nm and 589.6 nm. A diffraction grating with 531.5 lines per mm is used to observe the discrete spectrum of sodium. The angular separation between the D lines is 0.03 degrees. How far away would an observing screen need to be placed for the D lines to be separated by 1.0 mm? The answer I came up with is 3.2 mm but that does not seem correct. When the sodium vapor is placed under high pressure, additional spectral lines can be seen, most notably the 498.3 mm line and the 515 nm line. Using the same grating and distance above, what would be the vertical position of these lines on the screen?

Expert Solution

Distance of the screen can be simply calculated using

where, is in radians, r is the distance between screen and grating, l is the separation between 2 lines.

NOw

Using the grating equation

Thus, angular position of 498.3 nm and 515 m line will be

Thus, vertical distance/ separation will be

genius_generous answered 2 years ago

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