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

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SUMMARY

The discussion focuses on the mathematical relationship between the major and minor axes of an ellipse and the radius of a sphere within a cone of light. When a light source is positioned at height 'h' and a sphere with radius 'r' is placed at a vertical distance 'y' and a horizontal deviation 'x', the projection of the sphere onto a plane forms an ellipse if 'x' is not zero. The relationship between the ellipse's axes and the sphere's radius is crucial for understanding geometric projections in physics.

PREREQUISITES
  • Understanding of basic geometry, specifically ellipses and circles.
  • Familiarity with the concept of light cones in physics.
  • Knowledge of coordinate systems and spatial relationships.
  • Basic algebra for manipulating equations related to geometric shapes.
NEXT STEPS
  • Explore the mathematical equations governing ellipses, particularly the formulas for major and minor axes.
  • Study the properties of light cones and their geometric implications in physics.
  • Investigate the relationship between conic sections and their projections in three-dimensional space.
  • Learn about the applications of ellipses in optics and light behavior.
USEFUL FOR

This discussion is beneficial for students of physics, mathematicians, and anyone interested in the geometric properties of light and its projections, particularly in relation to ellipses and spheres.

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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