The wavelength of red light of potassium vapor is 768 nm. The distance from the middle of the central image

The wavelength of red light of potassium vapor is 768 nm. The distance from the middle of the central image of the grating slit to the first diffraction image is 13 cm, from the grating to the image 200 cm. Find the grating period.

For a grating with a period d, through which a plane light wave with a wavelength λ passes, the maximum illumination is observed at some angles φ:

dsinφ = mλ (m = 0, 1, 2,…), where m is the order of the main maximum.

We find the wavelength, taking into account that in our case m = 1:

d = mλ / sin φ;

d = λ / sin φ (1).

For small angles, the equality sinφ = tgφ is true. Find the angle tgφ:

tgφ = BC / AB = (0.13 m) / (2 m) = 0.065.

Substitute into formula (1):

d = (768 * 10 ^ -9 m) / 0.065 = 1.18 * 10 ^ -5 m = 0.018 mm.

Answer: d = 1.18 * 10-5 m (0.018 mm).