Consider two gratings. One grating has 3000 lines per cm, and the other one has 6000 lines per cm. Both gratings are illuminated with a beam of the same monochromatic light. Which grating produces the greater separation of colors?

In any grating, the position of bright fringe on the screen depends upon the

width of the fringe. In other words, distance between two consecutive bright

fringes depends upon fringe width. fringe width is given by the expression

/frac{/lambda D}{d}

Where λ is wave length of light used, D is distance of screen and d is d

is distance between two lines.

In the first case

d=/frac{1}{3000}//

=3.3/times 10^{-4}

In the second case

d = / frac{1}{6000}/ / cm

=1.67/times 10^{-4}cm

So d is less in the later case hence fringe separation will be greater. Colors will be separated widely in this case