Problem 1. In this problem we derive a formula [or the solid angle1 which is a measute ol the eld of View of an object from mule point P = (131, 112,133]. Here, we take the object to be a surfam 5'. The solid angle SHE} is the set of lines staiting at l\" and passing through S. We assume that such a line intersects S at most onoe1 as shown in the gure below. To measure the size of the solid angle, we plane a sphere mnteral at P and make the radius a small enough such that 5' appears hehind the sphere when seen from It Let 3(a) be the intersection of 9(3) with the Harlem: of the sphere. Then the measure of the solid angle is dened to be area of 5(a) n3 nus" ; The goal is to show that the solid angle (on alternatively he computed by the surlaoe integral |(3)l ; ff it was, .5- Irl' where r = (I. p1,:2 p2,13 p3} and [11,222,13} are the integration Vii-Tl- ahles. This formula shows that the denition of the measure of a solid angle is independent of the radius it of the sphere. 1You should show the mitliditgq.F of this formula with the following two steps. \f