Question

Visible light is incident perpendicularly on a diffraction grating of 200 rulings/mm. What are the (a) longest, (b) second longest, and (c) third longest wavelengths that can be associated with an intensity maximum at theta=30 degrees?

Answer 1

d•sinθ=k•λ
N₀=1/d =>
λ=sinθ/k•N₀
sin30°=0.5, N₀=2•10⁵ m⁻¹
k=1:
λ=sinθ/k•N₀=sin30°/1•2•10⁵=2.5•10⁻⁶ m
invisible - Infra-red
k=2
λ=sinθ/k•N₀=sin30°/2•2•10⁵=1.25•10⁻⁶ m
invisible - Infra-red

k=3
λ=sinθ/k•N₀=sin30°/3•2•10⁵=8.33•10⁻⁷ m
invisible - Infra-red
k=4 ….!!!!!
λ=sinθ/k•N₀=sin30°/4•2•10⁵=6.25•10⁻⁷ m
visible - red
k=5…. !!!!
λ=sinθ/k•N₀=sin30°/5•2•10⁵=5.0•10⁻⁷ m
visible - green
k=6 ….!!!!
λ=sinθ/k•N₀=sin30°/6•2•10⁵=4.17•10⁻⁷ m
visible - violet
k=7
λ=sinθ/k•N₀=sin30°/7•2•10⁵=3.57•10⁻⁷ m
invisible- ultra-violet