Consider a step$-$index optical fiber with a core refractive index of $1\mathrm{.}4522$; the difference between the core and cladding refractive index is $0\mathrm{.}36\%.$

$($a$)$ Compute the cladding refractive index, fractional index change $(\backslash$Delta $),$ and numerical aperture $($N$.$A$.).$