Suppose that there is a point light source illuminating a spherical surface; the point source moves towards the sphere with a constant speed of V; the distance to the sphere center at time t is h as shown in the figure. The radius of the sphere is R. The radiance intensity of the point source is I. (Radiance intensity = Power/solid angle) (a) Write the solid angle subtended by the sphere and the point source. (b) Write the total power received by the sphere. (c) Write the solid angle subtended by a differential surface dA at position (R,,) and the point source. (Note that (R,,) are defined according to conventional spherical coordinate system.) (d) If you integrate the power received by dA over the entire sphere, you should end up the result in Part (b) above. Write the integral and indicate the limits on and , but do not evaluate it. (e) Roughly plot the total power received by the surface as a function of time