A point source emits $200$ radiant watts and has a luminous efficacy of $120$ lumens$/$watt$.$ Its spatial distribution is spherically uniform.

a$)$ What is the luminous intensity of this source?

b$)$ What is the average illuminance on a unit sphere centered around the point source?

c$)$ What is the illuminance at point $p$ at the center of circular surface $A?$

d$)$ If surface A has a radius of $2m,$ what is the illuminance at point $q?$

e$)$ Explain why you think the previous result is correct.

f$)$ What is the total number of lumens incident onto surface $A?$

g$)$ The total reflectance of surface $A$ is $0\mathrm{.}50.$ What is the average exitance of surface $A?$

h$)$ Explain why you think the previous result is correct.