Question

What is most likely the color of the light whose second-order bright band forms an angle of 13.5° if the diffraction grating has 175 lines per mm?

green
red
violet
yellow

Answer 1

Use the grating equation d sinθ = mλ.

d = 1/(175 mm⁻¹) = 1/(175×10³ m⁻¹) = 5.714×10⁻⁶ m.
m = 2, θ = 13.5°, sin13.5° ≈ 0.23345.

λ = d sinθ / m = (5.714×10⁻⁶)(0.23345)/2 ≈ 6.67×10⁻⁷ m = 667 nm.

667 nm lies in the red part of the spectrum. Answer: red.