How can I show that the amplitude of a reflected wave?

[dam]

In Feynman Lectures on Physics (you can find it online), chapter 33 of volume 1, the author derives Fresnel's formulas for the coefficient of reflection in an unusual way by making considerations about the different possible polarization of light. In this way he derives the squares of the amplitudes of the reflected waves. When it comes to find the amplitude itself he says that it is possible to show by similar arguments that it must be real by considering two light rays coming from both sides of a glass surface simultaneously (he says that it is fun to analyze theoretically, I don't Know what does he mean by fun xD). I tried to use the same arguments to find the equations and then let the amplitude of one of the waves go to 0 to retrieve the original Solution, and I find indeed that the amplitude is the same, although I haven't yet managed to show it is the same derived by Feynman because of the horrible algebra. However I'm far from being sure that I've done everything alright so I wanted to ask if anybody knows How did the author mean to show it. Thank you in advance

 

[Simon Bridge]

Welcome to PF;
"The Author" in question meant for the student to figure it out.
"Horrible algebra" was par for the course in his day - students were expected to be good at algebra, the assignment was supposed to tax their abilities, and he did lecture at a top university.

Instead of trying to figure how Feynman would have done it, why not try seeing how it is usually taught today using a modern textbook?

 

[dam]

Actually I know how it is usually taught (Feynman himself uses the more common approach in the second volume), so it's not a problem of understanding the subject, it's just that I am curious to know how things that everybody think can only be shown by means of Maxwell's equations have actually other explanations.

 

[sophiecentaur]

Actually I know how it is usually taught (Feynman himself uses the more common approach in the second volume), so it's not a problem of understanding the subject, it's just that I am curious to know how things that everybody think can only be shown by means of Maxwell's equations have actually other explanations.

OK but please 'in addition to' ,not 'instead of'. :)

 

[sardar]

First of all, it is important to note that Feynman's approach to deriving Fresnel's formulas is not the only way to do so. There are other mathematical methods and physical interpretations that can also lead to the same results. However, Feynman's approach is unique and insightful, and it is worth exploring in detail.

In order to show the amplitude of a reflected wave, we must first understand what amplitude means in the context of waves. Amplitude refers to the maximum displacement or distance from equilibrium of a wave. In other words, it is a measure of the strength or intensity of the wave. In the case of a reflected wave, the amplitude is related to the amount of energy that is reflected back from a surface.

In chapter 33 of volume 1 of the Feynman Lectures on Physics, Feynman derives the squares of the amplitudes of the reflected waves using considerations about the different possible polarizations of light. This means that he considers the different orientations in which the electric and magnetic fields of the light wave can vibrate. He then uses these considerations to derive Fresnel's formulas for the coefficient of reflection, which relates the amplitudes of the incident and reflected waves.

To understand how Feynman shows that the amplitude of a reflected wave must be real, we must consider the concept of complex numbers. In physics, complex numbers are often used to represent the amplitudes of waves because they allow us to account for both magnitude and phase. In the case of a reflected wave, the amplitude would be a complex number with a real part and an imaginary part.

Feynman's approach involves considering two light rays coming from both sides of a glass surface simultaneously. He then shows that the amplitude of the reflected wave must be the same for both light rays. This means that the real and imaginary parts of the amplitude must be the same for both light rays. By considering the different possible polarizations of the incident and reflected waves, Feynman shows that the amplitude must be real.

Now, to address your attempt at using similar arguments to find the equations and retrieve the original solution, it is important to note that the algebra can be quite complicated and it is not necessary to go through all the steps in order to understand the concept. Instead, it may be more helpful to focus on the physical interpretation and logic behind Feynman's approach.

In conclusion, Feynman's approach to deriving Fresnel's formulas for the coefficient of