A diffraction grating has a resolving power . (a) We have to show that the corresponding frequency range that can just be resolved in given by . From the figure shown, we have to show that the “times of flight” of the two extreme rays differ by an amount ; (c) and that , which is independent of the various grating parameters. We may assume .
Solution: Click For PDF VersionFor light frequency and wavelength are related to each other through the speed of light c. We have the relation
From this relation we note that
The resolving for a grating is
The path difference between rays reaching the point P on the screen from two successive rulings of the grating is
If the grating has N rulings, the path difference between the extreme rays will be .
Assuming , we approximate it by .
Therefore, the difference in “times of flight” of the extreme rays will be
We thus find that