3. You can build a grating based spectrometer for atomic emission measurement of

Question

3. You can build a grating based spectrometer for atomic emission measurement of the sodium D lines. Suppose we have a blazed grating with 300 lines/mm,

1) at what angles will the first order maxima occur for these lines at an incidence angle of 30 degrees?

2) if the grating is a Littrow grating, which incidence angle should you use and what is the blaze angle for maximum efficiency in the first order?

Hint: maximum efficiency is achieved when each groove gives specular reflection.

3) calculate spectral resolving power for the Littrow grating. Can the grating be used to resolve the two Sodium D lines?

4) if a spectral resolution of 0.01nm is needed at a center wavelength of 590nm, which minimum diffraction order will you use with this grating? What is the free spectral range with that diffraction order? Hint: free spectral range corresponds to wavelength diffracted that exactly overlaps with the neighboring order.

Explanation / Answer

1) angles will the first order maxima occur = 60 and 90 degree

2) blaze angle for maximum efficiency in the first order = sin-1(0.35) + 60

                                                                               = 80.48 degree

3) spectral resolving power = [0.0035/(3.33 * 10-6)]

                                       = 1050

4)   minimum diffraction order    = 2nd

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