# How to determine the highest order of the spectrum of the diffraction grating

Passing through the grating the light beam is deflected from its direction at several different angles. As a result, on the other side of the bars of the brightness distribution pattern is obtained in which the bright areas alternated with dark. The whole picture is called diffraction spectrum, and the number of highlights in it determines the order of the spectrum.

## Instruction how to identify the highest order of the spectrum of the diffraction grating

Step 1:

The calculation is based on the formula, which relates the angle of incidence (α) on the diffraction grating, its wavelength (λ), the grating period (d), the diffraction angle (φ) and the order of the spectrum (k). In this formula, the product of the grating period of the difference between the sinuses and the diffraction angles of incidence is equal to the product of the order of the spectrum at a wavelength of monochromatic light: d * (sin (φ) -sin (α)) = k * λ.

Step 2:

Express from the above formula in the first step the order of the spectrum. As a result, you should have equality on the left side which will be the target value, and the right attitude is the product of the lattice period by the difference of sines two known angles to the wavelength of light: k = d * (sin (φ) -sin (α)) / λ.

Step 3:

Since the grating period, wavelength and angle of incidence of the resulting equation are constants, the order of the spectrum depends on the angle of diffraction. In the formula, it is expressed through the sinus and is the numerator of the formula. From this it follows that the greater the sine of this angle, the higher the order of the 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.

Step 4:

Substitute the numerical values of the conditions of tasks and calculate a specific 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 should in the numerator of the formula, so the greatest value of the spectrum obtained will be a period at the lowest value of the wavelength.