Considering a south$-$facing window shown in the attached figure with $W=1\mathrm{.}8m$ and $T=1\mathrm{.}0$ m at a latitude of $22N.($a$)$ How long should the overhang $($R$)$ be to allow $60\%$ transmission at solar noon, $75$ days on either side of June $21$ of an ordinary year. $($b$)$ Plot the variation of transmission factor over days at this place. $($note: similar to Fig. $2-13$ of the lecture notes$).$

$(20$ points$)$

$**$note: solar thermal energy course$**$