A diffraction grating with a period of 10 ^ 5 m is located parallel to the screen. At a distance of 20.88 cm

A diffraction grating with a period of 10 ^ 5 m is located parallel to the screen. At a distance of 20.88 cm from the center of the diffraction pattern, the maximum illumination is observed. Determine the order of this maximum.

d = 10 ^ -5m.

L = 1.8 m.

λ = 580 nm = 580 * 10 ^ -9 m.

a = 20.88 cm = 0.2088 m.

m -?

Let us write down the condition for observing the maximum for the diffraction grating: d * sinα = ± m * λ, where d is the period of the diffraction grating, m is the ordinal number of the maximum, λ is the wavelength of the illuminated light, ∠α is the angle between the beam that gives the maximum and the normal to screen.

For small angles sinα = tanα, therefore d * tanα = ± m * λ.

tgα = a / L.

The maximum condition will take the form: d * a / L = ± m * λ.

m = d * a / L * λ.

m = 10 ^ -5 m * 0.2088 m / 1.8 m * 580 * 10 ^ -9 m = 0.0002 * 10 ^ 4 = 2.

Answer: there is a maximum of the second order m = 2 on the screen.