Determine the constant of the diffraction grating if, when illuminated with light with a wavelength of 656 nm

Determine the constant of the diffraction grating if, when illuminated with light with a wavelength of 656 nm, the second spectrum is visible at an angle of 15.

Let’s start with a short entry given:

λ = 656 * 10 ^ -9 m;

sin φ = 0.25;

k = 2

To find:

d =?

To solve the problem, we apply the formula for the diffraction grating:

d * sinφ = k * λ,

where d is the grating period;

φ is the angle between the direction of the beam and the perpendicular to the screen;

k is the order of the spectrum.

We express the lattice period from the formula:

d = (k * λ) / sinφ.

It remains for us to substitute the values in the formula and perform the calculations.

So, we substitute and get:

d = (2 * 656 * 10 ^ -9) /0.25 = 5.2 * 10 ^ -6 m.

Answer: d = 5.2 * 10 ^ -6 m.