Diffraction Grating

Question

Violet light (410 nm) and red light (685 nm) pass through a diffraction grating with d=3.33*10^-6 m. What is the angular separation between them for m=2?

Answer 1

mλ = d sinθ

 

θ = sin^-1(mλ/d)

 

Violet:

 

λ = 410 x 10^-9 m

d = 3.33 x 10^-6 m

m = 2

 

θ = sin^-1[(2) (410 x 10^-9) / (3.33 x 10^-6)] ≅ 14.26°

 

Red:

 

λ = 685 x 10^-9 m

 

θ = sin^-1[(2) (685 x 10^-9) / (3.33 x 10^-6)] ≅ 24.29°

 

Δθ = (24.29 - 14.26)° = 10.03°