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The two point sources or two spectral lines of equal intensity are said to be ‘Resolved’ when the central maximum of the diffraction pattern due to one source falls on the first minimum of the diffraction pattern of the other source.
Let a parallel beam of light of wavelength λ and λ + dλ be incident, normally on a plane transmission grating element (a + b) and total number of rulings ‘N’. Let the diffracted beam be received by the telescope objective L. the total width is N (a + b) and total aperture of telescope objective is,
Let nth principal maxima of wavelength be formed in the direction , we have.
Let the first minima adjacent to the nth maxima be formed in the direction . Then form the grating equation of minima, we have
Clearly the first minima adjacent to nth principal maxima in direction increasing will be obtained if M = nN + 1.
According to Rayleigh’s criterion, two spectral lines of wavelength λ and λ + dλ are just resolved when nth maxima of wavelength λ + dλ falls on first minima of wavelength λ + dλ adjacent to its nth maxim. For nth maxima of wavelength λ, we have
Thus resolving power is independent of grating constant.
Dispersive power of a grating is given by
Therefore, the resolving power of a grating may be expressed as