Question

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)

Answer 1

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