MathDB

Let

C_1

and

C_2

be two concentric reflective hollow metal spheres of radius

R

and

R\sqrt3

respectively. From a point

P

on the surface of

C_2

, a ray of light is emitted inward at

30^o

from the radial direction. The ray eventually returns to

P

. How many total reflections off of

C_1

and

C_2

does it take?

Problem Statement