Question

Consider a room ten units long in the x, y, and z directions. Specically, the walls of the room are the four planes, x = 0, x = 10, y = 0, and y = 10, and the floor and ceiling are z = 0 and z = 10,respectively. A flat triangular mirror is mounted in one of the corners of the ceiling. The corners of the mirror are at locations (10; 9; 10), (10; 10; 9), and (9; 10; 10). You are sitting at location (5; 0; 0)
playing with your new green laser pointer.

(a) If you aim your laser pointer directly at the corner of the room with coordinates (10; 10; 10),
determine the coordinates where the beam will hit the walls, or
floor, of the room. (Hint: an
incoming ray of light, and the surface normal where the ray hits the surface, form a plane. The reflected ray is in the same plane. Also, the angle between the incoming ray and the normal is
the same as the angle between the normal and the reflected ray.)

(b) Suppose the flat mirror is replaced with one octant of a spherical mirror of radius 1. The corners
of the new spherical mirror are again located at (10; 9; 10), (10; 10; 9), and (9; 10; 10). If you
again aim your laser pointer directly at the corner of the room with coordinates (10; 10; 10),
determine the new coordinates where the beam will hit the walls, or floor, of the room. (Hint:
a sphere has the property that at a point P on the surface, the normal to the surface, n, is
parallel to the vector from the center of the sphere to the point P.)

Answer 1

THIS IS HARD

Answer 2

YES THIS IS HARD