Monochromatic light is normally incident on the diffraction grating, the wavelength of which (lambda) = 600 nm.

Monochromatic light is normally incident on the diffraction grating, the wavelength of which (lambda) = 600 nm. Determine the grating period if the third order maximum is observed at an angle (alpha) = 30 (degrees)

Given:
Lambda = 600 nm;
m = 3;
Angle alpha = 30 degrees.
Find: lattice period d.
Decision:
In order to solve the problem, you will need to use the formula for finding the diffraction grating. It looks like this: d * sinφ = m * λ.
It is necessary to express the period d from it, since this is what we need to find. We get: d = m * λ / sin φ.
We know that the sine of 30 degrees is 1/2, so it can replace the sine of the alpha with 0.5.
We substitute all the values in the formula and find the answer.
d = 3 * 600 * 10 ^ -9 / 0.5 = 3.6 * 10 ^ -6 m. Let’s translate into another system of calculation and get 3.6 microns.
Answer: 3.6 μm