Dispersion

The way in which the diffraction angle λβ behaves when light composed of different wavelengths is directed at a grating is an important point when considering the separation of light into its components. If the incident angle α is regarded as a constant, differentiating both sides of equation (2) with respect to λ gives the following:

Here, dβ/dλ is called the "angular dispersion" and can be used to obtain the change in diffraction angle dβcorresponding to a change in wavelength dλ. Multiplying both sides of equation (3) by the focal distance ƒ for the optical systems gives the following:

When ƒ·dβ = dx, inverting both sides of equation (4) gives the following:

Here, D is called the "reciprocal linear dispersion" and represents the difference in wavelength per unit length on the surface of the exit slit in the optical system. Multiplying D by the slit width gives an indication of the wavelength resolution.