$2)$ Calculate

a$.$ the average daylight factor $($ Da $)$ for the room in Figure $2$a$.$ The area of all surfaces $($floor$,$ ceiling, walls and windows$)$ of the room is $\backslash (66\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ and the area weighted average reflectance of all surfaces is $0\mathrm{.}5.$ The window in the room has a width of $2$ m and a height of $1$ m $.$ The visible transmittance of the glazing is $0\mathrm{.}8.$ There is a building opposite the window creating a visible sky angle of $\backslash (\backslash$theta $1=22^\{\backslash$circ$\}\backslash ).$

b$.$ The designer is not satisfied with the average daylight factor Da and increases the height of the window by $0\mathrm{.}5$ m $($see Fig. $2$b$).$ The visible sky angle becomes $\backslash (\backslash$theta $2=24^\{\backslash$circ$\}\backslash ).$ Calculate the new average daylight factor $($ Db $)$ and the increase $($in percentage$)$ of the average daylight factor.

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