# Explaining partial reflection of light as a wave

In QED by Richard Feynman, page 23 in the footnote; Feynman mentions that partial reflection is not an easy problem to tackle when we consider light as a particle and stated:

Those who believed that light was waves never had to wrestle with it.

Why?
If it was a mechanical wave I'd have tried to think about it as a typical collision problem with the wave losing some of its momentum causing the material to vibrate and some part of it gets reflected but what about electromagnetic waves?

Can you conceptually tell me why, if I consider light as a wave, partial reflection can be readily explained?

Thank you!

P.S I am not interested in how to calculate the probability of the reflection, the book goes through that, I just want to know why if I consider the light as a wave this won't be an issue.

• I don't know if you ever got your question answered but I understand where your going. You can't explain partial reflection with waves anymore than you can explain light waves without incorporating photons (particles). – Bill Alsept Mar 28 '17 at 22:43

A "wave" is a vague term, but known "wave" phenomena showed partial reflexion. So what is being said here is simply that there was strong experimental evidence of this effect for "wave" phenomena. So it's simply no surprise to someone who thinks light is some kind of "wave" that one gets partial reflexion.

There is also theoretical evidence too: more specifically and precisely, any disturbance $\psi(\vec{x}\,t)$ with the following two properties:

1. At all points, it is governed by D'Alembert's equation $\left(\nabla^2 - c^2\,\frac{\partial^2}{\partial t^2}\right)\psi = 0$ and $c$ possibly depends on position;
2. $\psi$ and its first derivatives are continuous across abrupt interfaces between regions of constant $c$

has solutions with partial reflexions at interfaces. Indeed, anywhere $c$ changes, there is a partial reflexion but, unless the change is abrupt or there is a Bragg-resonant periodic $c$ distribution, the reflexions tend to be six or more orders of magnitudes smaller than those from abrupt interfaces.

The Fresnel equations describe the same phenomena arising from Maxwell's equations.

Partial reflection of light in the quantum picture of photons is explained a certain probability for whole photons to be reflected as opposed to be transmitted. There is no partial reflection of a single photon. This probability corresponds to the intensity reflection coefficient of the corresponding electromagnetic wave.

• Thanks for the answer :) I know that but assume I am, wrongly, considering light as a wave only. How does this explain partial reflection as Feynman pointed out? – Fingolfin Dec 13 '16 at 5:11
• @xci13 - Feynman probably talks about the determination of this reflection probability by calculating the microscopic interaction of a photon with the atoms of the reflector. – freecharly Dec 13 '16 at 5:19
• He does :) that's not the question. The question is why this won't be an issue if we thought life was a wave. – Fingolfin Dec 13 '16 at 5:25
• @xci13 Considering light as an electromagnetic wave, and the reflector as a medium with different refractive index, makes it, of course, easy to calculate the reflection factor and thus probability. – freecharly Dec 13 '16 at 5:30

I had the same question when i read the book. I think that it is easy to explain partial reflection of a wave because a wave is basically a transmission of energy. so it is not unexpected for some energy to be transmitted and some to be reflected. the same cannot be said for a photon particle. for a photon particle to go through the glass is puzzling, unless the glass has holes or pores (as Feynman also mentions and disproves in the same book)