Two slits of width $2$m$,2$m$,$ each in an opaque material, are separated by a center$-$to$-$center distance of $6$m$\mathrm{.}6$m$.$ A monochromatic light of wavelength $450$ nm is incident on the double$-$slit. One $$nds a combined interference and diffraction pattern on the screen.

$($a$)$ How many peaks of the interference will be observed in the central maximum of the diffraction pattern?

$($b$)$ How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same?

$($c$)$ How many peaks of interference will be observed if the slits are separated by twice the distance, that is$,12$m$,12$m$,$ while keeping the widths of the slits same?

$($d$)$ What will happen in $($a$)$ if instead of $450-$nm light another light of wavelength $680$ nm is used?

$($e$)$ What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in $($a$)?$

$($f$)$ Does this ratio depend on the wavelength of the light?

$($g$)$ Does this ratio depend on the width or separation of the slits?