The calculation is based on the formula that relates the angle of incidence (α) to a diffraction grating, its wavelength (λ), the period lattice (d), the diffraction angle(φ) and order spectrum (k).In this formula, the product of a period lattice the difference between the sines of the angles of incidence and diffraction equal to the product of the order spectrum at a wavelength of monochromatic light: d * (sin (φ) -sin (α)) = k * λ.
Express from the above formula in the first step of the procedure spectrum .As a result, you should have equality on the left side which will be the unknown quantity, and the right attitude
to the work period lattice the difference sine two known angles to the wavelength of light: k = d * (sin (φ) -sin (α)) / λ.
Since the grating period , wavelength and angle of incidence of the resulting equation are constants, order spectrum depends only on the angle of diffraction.In the formula, it is expressed in terms of sine and is the numerator of the formula.From this it follows that the more the sine of the angle, the higher the order spectrum .The maximum value that can take the sine is equal to one, so just replace in the formula sin (φ) to yedinichku: k = d * (1-sin (α)) / λ.This is the ultimate formula for calculating the maximum value of the order of the diffraction spectrum .
Substitute numerical values ​​of the conditions of the problem and calculate the particular value of the desired characteristics of the diffraction spectrum .The baseline can be said that the incident light on the diffraction grating is composed of several colors with different wavelengths.In this case, the use in the calculations of these, which is of less importance.This value is the numerator of the formula, so the period of greatest value spectrum is obtained with the lowest value of the wavelength.