Three discrete spectral lines occur at angles of 10.2 degree, 13.8 degree, and 1

Question

Three discrete spectral lines occur at angles of 10.2 degree, 13.8 degree, and 14.9 degree, respectively, in the first-order spectrum of a diffraction grating spectrometer. (a) If the grating has 3760 slits/cm, what are the wavelengths of the light? lambda_1 = 470 nm (10.2 degree) lambda_2 = 634.39 nm (13.8 degree) lambda_3 = 683.86 nm (14.9 degree) (b) At what angles are these lines found in the second-order spectra? theta = 10.2 degree (lambda_1) theta = 13.8 degree (lambda_2) theta = 14.9 degree (lambda_3)

Explanation / Answer

b)

Formula for grading diffraction is

Dsin = m

m – order of the spectrum = 2

D – one slit thickness = 1/3760 slits/cm = 1/376000 m

= arcsin(2/D)

1 = arcsin(2 x 470 x 10-9 x 376000)

1 = 20.7o

2 = arcsin(2 x 634.39 x 10-9 x 376000)

2 = 28.5o

3 = arcsin(2 x 683.86 x 10-9 x 376000)

3 = 30.9o

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