Determine the number of grooves per 1 cm of the diffraction grating, if at normal incidence of light with a wavelength

Determine the number of grooves per 1 cm of the diffraction grating, if at normal incidence of light with a wavelength of 600 nm the grating gives the first maximum at a distance of 3.3 cm from the central one. The distance from the grate to the screen is 110cm.

General formula for a diffraction grating:
d * sin f = ± kl (k = 1, 2, …),
where d is the grating period, f is the angle at which the maximum is visible, k is the number of the maximum, L is the wavelength.
For k = 1:
d * sin f = L;
sin f = L / d;
d = L / sin f;
If you build a triangle on the segments a = 110 cm and b = 3.3 cm, then the hypotenuse c = root (3.3 ^ 2 + 110 ^ 2) = 110.05.
sin f = b / c = 3.3 cm / 110.05 = 0.03;
d = 0.0000006 m / 0.03 m = 0.00002 m.
The number of lines per centimeter:
N = 0.01 m / 0.00002 m = 500 strokes.
Answer: 500 lines / cm.