One can also use ray tracing and parallax to find the images within spherical mirrors. One uses the conditions for the shortest path to determine the reflection points on the sphere. The intersection of two rays can then be used to determine the parallax position of the source image.
One can use path lengths to determine the surfaces of constant action. The directions of the final rays are all perpendicular to these surfaces. The image point within the sphere varies with the position of the observer.
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