## Description

1) a) What is the solid angle subtended by the moon as viewed from the earth if we assume the

moon to be a sphere of radius R at a distance d?

b) What is the range of possible solid angles subtended by a flat circular plate of radius R at a

distance d?

2) Consider a room in the shape of a cube of dimension 100 feet × 100 feet × 100 feet. Consider

a square patch of size 1 foot by 1 foot on the ceiling. Suppose that the patch is exactly in the

center of the ceiling.

a) What is the foreshortened area of the square patch as viewed from a corner of the room on

the floor?

b) What is the solid angle subtended by the square patch as viewed from a corner of the room

on the floor?

c) What is the solid angle subtended by the square patch as viewed from a corner of the room

on the ceiling?

3) Consider a Lambertian plane in three dimensions defined by the equation

7x +

√

50y + z + 2 = 0

a) What is the surface gradient (p, q) for the plane?

b) Suppose that the plane is in a dark room with a single point light source. Consider the point

P = (0, 0, −2) on the plane. Determine the location (x, y, z) where we should put the point light

source so that the light source is a distance 20 from the point P and the reflected radiance from

P in the direction of (0, 0, 0) is as large as possible.