Answer
$9$
Work Step by Step
The angular locations of the diffraction minima are given by
$a\sinθ=mλ$
For first diffraction minima
or, $\sinθ=\frac{λ}{a}\;$.........(1)
The angular locations of the bright fringes of the double-slit interference pattern are
given by
$d\sinθ=mλ$
Substituting eq. 1, we obtain
$d\frac{λ}{a}=mλ$
or, $m=\frac{d}{a}$
Substituting the known values, we obtain,
$m=\frac{0.15\times10^{-3}}{30\times10^{-6}}$
or, $m=5$
Thus the $m=5$ bright fringe in the both side of the central bright fringe is eliminated by the first-order diffraction minima.
Therefore, including the central bright fringe and the fringes on the both side of it, there are (4+1+4)=9 bright fringes between the first diffraction-envelope minima.
