Problem $3[$Front$-$back$-$focal points and principal planes $20\%]$

A thick lens has each of radius $5cm$ to incident light, as shown in Fig. $2.$ The lens is $1\mathrm{.}5cm$ thick and

has a refractive index of $1\mathrm{.}33.$ Find $($a$)$ the system matrix for the lens when used in air and $($b$)$ front and

back focal points $($c$)$ principal planes $P_1$ and $P_2$ and $($d$)$ Effective focal length $f_{\text{e}\text{f}\text{f}}.$

Fig. $2.$ Problem $3.$