c$)$ A small surface of area $A_1={10}^{-3}{m}^2$ is known to emit diffusely, and from measurements the total intensity associated with emission in the normal direction is $I_n=7000\frac{W}{m^2}.$sr$.$

Radiation emitted from the surface is intercepted by three other surfaces of area $A_2=A_3=A_4={10}^{-3}{m}^2,$ which are $0\mathrm{.}5$ m from $A_1$ and are oriented as shown in Fig. Q$4.$

i$)$ What is the intensity associated with emission in each of the three directions?

$(4$ marks$)$

ii$)$ What are the solid angles subtended by three surfaces when viewed from $A_1?$

$(9$ marks$)$

iii$)$ What is the rate at which radiation emitted by $A_1$ is intercepted by the three surfaces?

$(12$ marks$)$