We have to derive the following expression for the intensity pattern for a three-slit “grating”:
|
Solution: Click For PDF Version As the slit-width ,
where
is the wavelength of the light incident on the three-slit
“grating”, we will ignore the effect on the intensity of
the principal maxima due to the diffraction envelope produced
because of the finite size of the slits. Further, we will assume
that the magnitude of the amplitudes of the electric field vectors
at the same point on the screen due to each of the three slits is
equal.
We
recall that the phase difference between two rays reaching a point
on the screen at an angle
The path
difference between rays from two successive slits is
From the
superposition principle the electric field at a point P
at an angle
where
We find that
In the above
expression using
The intensity of electromagnetic wave is proportional to the square of modulus of the amplitude of its electric field vector and is given by the expression
The central
maximum is at
|
from two slits separated by a distance d
is related to their path difference as
.
Therefore,
.
,
we find that
.
The intensity of the central maximum will therefore be