We
consider a double-slit each of width a
and let their separation
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Solution: Click For PDF Version (a)The intensity pattern of a double-slit of slit separation d and size of each slit a is given by the equation
where
We note that the central diffraction envelope is determined by the condition that
Therefore, the angular size of the principal diffraction envelope is
Interference fringes are determined by the Young’s double-slit interference condition
We are given
that
Therefore,
for
we note that
And,
We note that
for
(b)
If
And,
which is the intensity of diffraction of a single slit of width 2a.
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.
(a) We have to find the interference fringes
that lie in the central diffraction envelope.
(b) If we put
,
the two slits coalesce into a single slit of
width 2a.
We have to show that the formula for the
intensity of a double-slit with slits of finite size reduces to the
diffraction pattern for such a slit.
,
,
therefore two fringes corresponding to
,
,
and at this point we have the diffraction minima of the central
envelope. Therefore, the total number of fringes contained inside
the central envelope is three.
