Using the equation for the distance between fringes, $\backslash (\backslash$Delta y$=\backslash$frac$\{$x $\backslash$lambda$\}\{$d$\}\backslash ),$ complete the following.

$($a$)$ Calculate the distance $($in cm $)$ between fringes for $612$ nm light falling on double slits separated by $0\mathrm{.}0200$ mm $,$ located $3\mathrm{.}40$ m from a screen.

$\backslash [$

$\backslash$mathrm$\{$cm$\}$

$\backslash ]$

$($b$)$ What would be the distance between fringes $($in cm $)$ if the entire apparatus were submersed in water, whose index of refraction is $1\mathrm{.}333?$

cm