A student installs a double$-$slit assembly $1\mathrm{.}45$ m from a viewing screen. The slits are separated by $0\mathrm{.}0584$ mm$.$

$($a$)$

Suppose the student aims a beam of yellow light, with a wavelength of $589$ nm$,$ toward the slit assembly, and this makes an interference pattern on the screen. What distance $($in cm$)$ separates the zeroth$-$order and first$-$order bright fringes $($a$.$k$.$a$.$ maxima$)?$

cm

$($b$)$

Now suppose that blue light $($with

$=413$ nm$)$

is used instead. What distance $($in cm$)$ will now separate the second$-$order and fourth$-$order bright fringes?

cm