Question

Light with a wavelength of about 490 nm is made to pass through a diffraction grating. The angle formed between the path of the incident light and the diffracted light is 9.2° and forms a first-order bright band.

What is the number of lines per mm in the diffraction grating? Round your answer to the nearest whole number.

lines per mm

Answer 1

Use the grating equation mλ = d sinθ with m = 1, λ = 490 nm, θ = 9.2°.

d = λ / sinθ = 490×10^−9 m / sin(9.2°) ≈ 490×10^−9 / 0.159881 ≈ 3.0637×10^−6 m.

Lines per mm = 1/(d in mm) = 1/(3.0637 μm) = 1/(0.0030637 mm) ≈ 326.47 ≈ 326 lines per mm.