# Reflection of a Point Object in an Arbitrary Curved Mirror

## TL;DR

This paper derives the mathematical equation for the reflection curve of a point object in any arbitrary curved mirror using basic optics laws and coordinate geometry, comparing results with Gaussian optics and standard mirror formulas.

## Contribution

It provides a new general equation for the reflection curve in arbitrary curved mirrors, extending classical optics to more complex geometries.

## Key findings

- Derived the reflection curve equation for arbitrary curved mirrors.
- Validated the equation with examples and Gaussian optics comparison.
- Showed reduction to standard mirror formula under paraxial approximation.

## Abstract

In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection of classical geometric optics and elementary coordinate geometry. Several examples are provided and compared with Gaussian optics. We also see how the equations reduce to the standard mirror formula under the paraxial approximation.