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(A) The fringe width $\beta$ in Young's double slit experiment is given by $\beta = \frac{D\lambda}{d}$,where $D$ is the distance to the screen,$d$ is

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Statement-$1$ is true,Statement-$2$ is true,and Statement-$2$ is the correct explanation of Statement-$1$.

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(A) The fringe width $\beta$ in Young's double slit experiment is given by $\beta = \frac{D\lambda}{d}$,where $D$ is the distance to the screen,$d$ is the slit separation,and $\lambda$ is the wavelength.The number of fringes $N$ that can be observed in a field of view of width $W$ is given by $N = \frac{W}{\beta} = \frac{Wd}{D\lambda}$.From this relation,$N \propto \frac{1}{\lambda}$. Thus,as the wavelength $\lambda$ increases,the fringe width $\beta$ increases,and the number of fringes $N$ observed in the field of view decreases. Conversely,for a shorter wavelength,the fringe width is smaller,allowing more fringes to be observed.Therefore,Statement-$1$ is true,Statement-$2$ is true,and Statement-$2$ provides the correct explanation for Statement-$1$.

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