Answer
$13$
Work Step by Step
The angular locations of the diffraction minima are given by
$a\sin\theta=m\lambda$
For first diffraction minima
or, $\sin\theta=\frac{\lambda}{a}\;.........(1)$
The angular locations of the bright fringes of the double-slit interference pattern are
given by
$d\sin\theta=m\lambda$
Substituting eq. 1, we obtain
$d\frac{\lambda}{a}=m\lambda$
or, $m=\frac{d}{a}\;$
Substituting the known values, we obtain,
$m=\frac{0.3\times10^{-3}}{46\times10^{-6}}$
or, $m=6.52$
Therefore, including the central bright fringe and the fringes on the both side of the central, there are $(6+1+6)=13$ bright fringes between the two first-order minima
of the diffraction pattern.
