The Crystal Cave Mirror · AI Generator #GEN-7FAF8FD0
Physics · optics
Problem
Deep in a cave, a geologist discovers a remarkable crystal formation: a solid transparent crystal sphere of radius R=8.0cm with refractive index n=1.5, resting on the cave floor. The sphere has a small air bubble of radius r=1.0cm located at distance d=3.0cm from the sphere's center, along a line connecting the center to the point where the geologist's laser pointer enters the crystal.
The geologist shines a narrow laser beam horizontally into the crystal sphere. The beam enters the sphere at the point closest to the air bubble (along the line connecting the sphere center to the bubble center) and travels in a straight line toward the bubble. When the light ray hits the curved surface of the air bubble, it undergoes total internal reflection.
After this reflection from the bubble surface, the light ray travels through the crystal and exits the sphere. Find the angle θ (in degrees) that the exiting light ray makes with the horizontal, measured counterclockwise from the positive horizontal direction.