Reflection off Surfaces of Revolution: a Teachers' primer to the Introduction of the Cross-section Concept

TL;DR

This paper introduces a calculus-based method for calculating the differential cross-section of light reflection off convex surfaces of revolution, suitable for undergraduate physics education, with illustrative examples.

Contribution

It presents a novel, elementary calculus approach to calculating reflection cross-sections for convex surfaces of revolution, tailored for teaching introductory physics courses.

Findings

Method applicable to various convex surfaces of revolution

Provides clear examples for classroom discussion

Facilitates understanding of physical properties of reflection cross-sections

Abstract

The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is therefore suitable for calculus oriented introductory undergraduate university physics courses. Three particular cases are presented as examples of the general procedure and of the physical properties and considerations about cross-sections they allow to discuss in class.