A
diffraction grating has a resolving power
|
Solution: Click For PDF Version For 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
We have
(b) 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
Therefore, the difference in “times of flight” of the extreme rays will be
(c) We thus find that
|
.
(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
.
.
.
.
