This series of short videos shows how to derive Maxwell’s equations all the way to Fresnel’s equations. Each one is about 10 to 15mn long.

The first four videos show how to use boundary conditions to deduce the relationship between the electromagnetic field on both sides of a surface (or interface between two different media).

• Electromagnetic Boundary Conditions Explained
• Normal Electric Field Boundary Conditions
• Tangential Magnetic Field Boundary Conditions
• Normal Magnetic Field Boundary Conditions

The next four videos use the previous results to obtain the Fresnel equations, for S-polarized and P-polarized cases.

• Wave Impedance Explained
• Fresnel Equations at Normal Incidence
• Fresnels Equations at an Angle
• Fresnels Equations for p-Polarized Waves

The rest of the series then dives into other topics like thin film interference.

The series assumes the viewer to be already familiar with the Maxwell equations, so it can be helpful to first see the explanation by Grant Sanderson of 3Blue1Brown on Maxwell’s equations.