The diffraction grating has 50 lines per millimeter. At what angle is the maximum

The diffraction grating has 50 lines per millimeter. At what angle is the maximum of the second order of monochromatic radiation with a wavelength of 400 nm visible?

We use to solve the formula describing the diffraction grating: d * sin φ = k * λ, where

d – diffraction grating constant;

d = 1/50 = 0.02 mm. = 2 * 10 ^ -5 m.

sin φ is the sine of the angle of deviation from the straight-line passage of light,

k is the order of the lattice maximum,

λ is the length of the light wave.

sin φ = k * λ / d = 2 * 400 * 10 ^ -9 / 2 * 10 ^ -5 = 400 * 10 ^ -4 = 0.04;

φ = arcsin 0.04;

φ = 2 ° 17 ‘.