Q. With necessary theory explain the formation of spectrum by a plane transmission grating when composite light falls on it

OR

How does plane diffraction grating forms a spectrum? On which factors does the width of a spectral line depends?

When a beam of light of wavelength falls normally on a grating the principle maxima are formed in the direction given by

From equation (1) it is clear, that for a given order n, the angle of diffraction '?' varies with l.  As the wavelength increases, the angle of diffraction also increases.

Hence if white light is incident on grating, then each order will contain principle maxima of different wavelength in different direction. The principle maxima of all wavelength corresponding to will form the first order spectrum and so on.

The principle of maxima of all wavelength corresponding to will however be along the same direction. Hence, the zero order maxima will be white having on either side of it first order spectrum, second order spectrum and so on. Most of light is concentrated in the zero order principle maxima and the intensity goes on gradually decreasing as we move towards higher order spectrum. As we know the secondary maxima are not necessary to be seen.

The factor on which the width of spectral line depends : The angular width is inversely proportional to the total number of lines ruled on the grating and order of principal maxima and directly proportional to ?n. since the increase in ?n is less than the increase in n, therefore the angular width of principle maxima decreases for higher values of n.