Question

If the distance between slits on a diffraction grating is 0.50 mm and one of the angles of diffraction is 0.25°, how large is the path difference?


nm



How many orders of bright lines does this equal for red light with a wavelength of 650 nm?


wavelength

Answer 1

Path difference = d sinθ = (0.50 mm) sin(0.25°).

sin(0.25°) ≈ 0.0043633, so
path difference = 5.0×10−4 m × 0.0043633 ≈ 2.18×10−6 m = 2.18×10^3 nm ≈ 2180 nm.

Number of wavelengths for λ = 650 nm: m = (path difference)/λ ≈ 2180/650 ≈ 3.36.
Thus this corresponds to the 3rd order bright line (m = 3; m must be an integer ≤ 3.36).