What is Rayleigh’s criterion of resolution? Define resolving power of grating?

Answer: Two point sources (or spectral lines) are just resolved when the principal maximum of one falls on the first minimum of the other. Resolving power of a grating \(=\frac{\lambda}{d\lambda}=nN\).

Rayleigh's criterion: Two closely spaced point sources or spectral lines of equal intensity are said to be just resolved by an optical instrument when the central (principal) maximum of the diffraction pattern of one falls exactly on the first minimum of the diffraction pattern of the other, and vice versa. If they are closer than this, the patterns merge and they cannot be seen as separate.

Resolving power of a grating: It is the ability of the grating to separate two spectral lines of very close wavelengths. It is defined as the ratio of the wavelength \(\lambda\) of a spectral line to the smallest difference in wavelength \(d\lambda\) between this line and a neighbouring line such that the two are just resolved:

\[\text{R.P.}=\frac{\lambda}{d\lambda}=nN\]

where \(n\) = order of the spectrum and \(N\) = total number of lines (rulings) on the grating. So the resolving power increases with the order and with the total number of lines, and does not depend on the grating element.