Exploring the Relationship Between Ellipse & Sphere's Radius in Cone of Light

AI Thread Summary
The discussion focuses on understanding the geometric relationship between the axes of an ellipse and the radius of a sphere within a cone of light. It highlights that when a light source is positioned at a height 'h' above a plane, and a sphere of radius 'r' is placed at a vertical distance 'y' and a horizontal deviation 'x', the projection changes based on this deviation. Specifically, when there is no horizontal deviation, the projection is circular, but the inquiry seeks to establish how the ellipse's major and minor axes relate to the sphere's radius when deviation occurs. The conversation emphasizes the need for mathematical insights to clarify this relationship. Overall, the discussion aims to bridge concepts of geometry and light projection.
Chandi
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Hi everybody,

Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light.

For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of 'r') is located at y vertical distance from the source of light and horizontally deviated at x distance from the perpendicular axis of the plane and the source of light.
Obviously if the horizontal deviation is zero, then the projection is a circle. But I would like to know the relationship of the ellipse to the radius of the sphere when horizontal deviation is not zero.
 
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This question belongs in the math section.
 
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