Suppose that you have a reflection diffraction grating with 135 lines per millim

Question

Suppose that you have a reflection diffraction grating with 135 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen
a)Two visible lines in the sodium spectrum have wavelengths 498nm and 569 nm. What is the angular separation of the first maxima of these spectral lines generated by this diffraction grating?
Express your answer in degrees to two significant figures
b)How wide does this grating need to be to allow you to resolve the two lines 589.00nm and 589.59nm nanometers, which are a well known pair of lines for sodium, in the second order ()?
Express your answer in millimeters to two significant figures.

Explanation / Answer

No.of lines per mm = 135 grating element d = 1/ 135 = 7.407*10^-3 mm     d = 7.407*10^-6 m wavelengths = 498 * 10 ^-9 m                   ' = 569 * 10 ^-9 m condition for 1 st maximum d sin = from this sin = / d                       = 0.06723                    = 3.854 degrees for wavelength ': ------------------ d sin ' = '    sin ' = ' / d              = 0.0768         ' = 4.405 degrees So, angular separation = ' -= 0.55 degrees (b).wavelengths = 589 nm                          ' = 589.59 nm order n = 2 we know " / d = nN   [(+')/2] / ['-] = 2 N 589.295/0.59 = 2 N                  N = 499.4 ~ 500

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