The Crystal Ball Camera · AI Generator #GEN-AB18BD2B
Physics · optics
Problem
A photographer uses a solid glass sphere (refractive index n=1.5) of radius R=5.0cm as an artistic lens element. She places a small object at distance d=15cm from the center of the sphere, on the side facing her camera. Light from the object enters the sphere, undergoes refraction at both surfaces, and emerges on the camera side.
(a) Find the distance from the sphere's center to the final image location.
(b) Determine the overall magnification of this optical system.
Treat the glass sphere as two refracting surfaces in sequence: first the object-side surface (convex toward the object), then the camera-side surface (convex toward the camera). Use the convention that distances are positive when measured in the direction of light propagation.