Imaging in Reflecting Spheres

TL;DR

This paper investigates how images are formed in a reflective sphere using caustics, revealing two images with partial focus and verifying their existence experimentally across different configurations.

Contribution

It introduces a detailed analysis of image formation in reflective spheres, including the concept of viewable surfaces and experimental verification of image positions.

Findings

Two images form with partial focus along principal directions.

The distance between images matches theoretical calculations.

Experimental results confirm the predicted image positions.

Abstract

We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system is, in general, a Gaussian surface with partial focus along the two principal directions of the Gaussian surface; i.e. there are two images of the source point, each with partial focus. As the source point moves, the images move on two surfaces, referred to as \emph{viewable surfaces}. In our systems, one viewable surface consists of points with radial focus and the other consists of points with azimuthal focus. The problems we study are (1) imaging of a parallel beam of light, (2) imaging of the infinite viewed from a location outside the sphere, and (3) imaging of a planar object viewed through the point of its intersection with the radial line normal to the plane. We verify the existence of two images experimentally and show that the distance between them agrees with the computations.