# Why history matters: ab initio rederivation of Fresnel equations confirms microscopic theory of refractive index

## TL;DR

This paper critically reexamines the derivation of Fresnel equations, revealing contradictions with traditional macroscopic theory, and offers a new derivation based solely on microscopic Maxwell equations aligned with modern physics.

## Contribution

It provides a microscopic rederivation of Fresnel's equations and proposes the most general boundary conditions for electric and magnetic fields at microscopic interfaces.

## Key findings

- Standard Fresnel equations contradict macroscopic electrodynamics.
- Microscopic derivation aligns with first-principles physics.
- Proposes general boundary conditions for fields at microscopic boundaries.

## Abstract

We provide a systematic theoretical, experimental, and historical critique of the standard derivation of Fresnel's equations, which shows in particular that these well-established equations actually contradict the traditional, macroscopic approach to electrodynamics in media. Subsequently, we give a rederivation of Fresnel's equations which is exclusively based on the microscopic Maxwell equations and hence in accordance with modern first-principles materials physics. In particular, as a main outcome of this analysis being of a more general interest, we propose the most general boundary conditions on electric and magnetic fields which are valid on the microscopic level.