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?

Explanation:

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

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