The dispersive power of a diffraction grating is defined as the rate of change of the angle of diffraction with the wavelength of light. It is denoted by
For plane transmission grating, we have
where (a +b) is the grating element and θ is the angle of diffraction for nth spectrum, differentiating (1) with respect to λ, we get
Hence Dispersive power,
Here “dλ” is the angular separation between two lines having wavelength difference dλ.
- The dispersive power is directly proportional to n i.e. the order of the spectrum. Thus higher is the order, greater is the dispersive power.
- The dispersive power is inversely proportional to the grating element (a + b). This means that the dispersive power is directly proportional to the number of lines per cm of the grating.
- The dispersive power is inversely proportional to Cos θ. Thus if the angle of diffraction θ = 0, Cos θ = 1 and so the angular dispersive is minimum. Therefore if θ is 0 small, the value of Cos θ may be neglected.
Thus the angular dispersion of two spectral lines in a particular order is directly proportional to the difference in wavelength between the two spectral lines.
Linear dispersive power
If dx is the linear separation of two spectral lines differing in wavelength dλ in the focal plane of a lens of focal length f, we have
dx = f dθ