Answer to Question #81583 in Physics for cc7

Question

1. Three discrete spectral lines occur at angles of 10.5°,13.7°, and 14.9°, respectively, in the first-order spectrum of a diffraction grating spectrometer.

(a) If the grating has 3685 slits/cm, what are the wavelengths of the light?

(b) At what angles are these lines found in the second-order spectra?
θ=° (λ1)
θ=° (λ2)
θ=° (λ3)

Answer 1

(a) If the grating has 3685 slits/cm, what are the wavelengths of the light?
d sin(θ) = n λ
n=1
d=〖10〗^(-2)/3685=2.7137∙〖10〗^(-6) m
λ_1=2.7137∙〖10〗^(-6) sin⁡〖10.5°〗=495 nm.
λ_2=2.7137∙〖10〗^(-6) sin⁡〖13.7°〗=643 nm.
λ_3=2.7137∙〖10〗^(-6) sin⁡〖14.9°〗=698 nm.
(b) At what angles are these lines found in the second-order spectra?
θ_1=sin^(-1)⁡(2(495)/2713.7)=21.4°
θ_2=sin^(-1)⁡(2(643)/2713.7)=28.3°
θ_3=sin^(-1)⁡(2(698)/2713.7)=31.0°