Determine the period of the diffraction grating, on which light with a wavelength λ = 550nm

Determine the period of the diffraction grating, on which light with a wavelength λ = 550nm is normally incident. It is known that the fifth-order maximum is observed at an angle a = 30 °.

The grating period and the angles at which the intensity maxima are observed are related by the ratio:

d sin φ = kλ,

where d is the lattice period,

φ is the angle at which the maximum is observed,

k – order of maximum (0, ± 1, ± 2 …)

λ is the wavelength.

d = kλ / sin φ = 5 * 550 nm / sin 30 ° = 5 * 550 nm / 0.5 = 5500 nm = 5500 * 10-9 m = 5.5 * 10-6 m = 5.5 microns.

Answer: 5.5 * 10-6 m (5.5 microns).