Three discrete spectral lines occur at angles of 10.1°, 13.7°, and 15.0°, respectively, in the first-order spectrum of a diffraction grating spectrometer.
(a) If the grating has 3670 slits/cm, what are the wavelengths of the light?
λ1 = ?nm (10.1°)
λ2 = ?nm (13.7°)
λ3 = ?nm (15.0°)
(b) At what angles are these lines found in the second-order spectra?
θ = ?° (λ1)
θ = ?° (λ2)
θ = ?° (λ3)
d = 0.01/ 3670 =2.72479564e-6
d*sin ( 10.1) = λ1
λ1 =2.72479564e-6* sin ( 10.1 ) =477.83 nm
λ2 = 2.72479564e-6* sin ( 13.7) = 645.336 nm
λ3 =2.72479564e-6* sin ( 15) = 705.22 nm
b)
d*sin(θ) = 2* λ1
θ1 = asin (2* λ1/ d) = asin( 2*477.83*10^-9/ ( 2.72479564e-6)) = 20.53deg
θ2 = asin (2* λ2/ d) = asin( 2* 645.336 *10^-9/ ( 2.72479564e-6)) = 28.27 deg
θ3 = asin (2* λ3/ d) = asin( 2*705.22 *10^-9/ ( 2.72479564e-6)) = 31.17 deg
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