Fresnels Equations at an Angle

/ edmundsj
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It's great to be able to calculate waves which reflect off that are normal to a surface, but what about waves at an angle? This video covers s-polarized waves reflecting off an interface, and I derive Fresnel's Equations from the previously-discussed boundary conditions.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.

[@meetoptics]

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[@eastofthegreenline3324]

This series is great and I often return to it to refresh my memory. One thing I didn't notice first time was at 10:36 you refer to the plane of the blackboard as the "plane of incidence." Hecht (Optics) likewise. It is the plane in which we see the angle of incidence but I am wondering if the term originally referred to the plane to which k is normal? After all the light is incident along k...At any rate your video clarified this. Tks!

[@ankusingh1954]

What a great explanation. Thank you so much sir 🙏🙏😍😍

[@alihussein1005]

Wonderful Explanation! Thx a lot

[@adiazdu]

Awsome! Your videos are so helful for me :) thanks.

[@meetoptics]

They are for sure!

[@matheshvaithiyanathan3372]

It's short and sweet.

[@meetoptics]

So good. Completely agreed 🚀

[@vegardnybakeri8148]

Wow this is great!

[@meetoptics]

It is amazing, sure!

[@adiazdu]

I have a question. What happens if the interface that I am interested to study has some charge density (so changing the boundary conditions)... can I (for some reason) still apply the Fresnel’s equations derived here? Regarding that my boundary conditions are going to be different.

[@JordanEdmundsEECS]

No, you will have to include the charge density term in the derivation of Fresnel’s equations, so they would be different. You can definitely do it though, it’s just r and t will be different.

[@adiazdu]

Thanks

[@adiazdu]

Actually, when looking at this problem, I just realised that my boundary conditions are going to change for the electric field normal to the surface, and when deriving the Fresnel’s equations we only use the tangential electric field, so, taking it into account, the Fresnel’s equations are going to be the same, is that right?

[@meetoptics]

@@adiazdu it is great, true! Thanks again

[@yimmakofa7020]

How do we derive an expression for reflectance as a function of angle of incidence for thin film coating? Thanks

[@mytrusmars]

Great 👍

[@varkush399]

proof of me paid attention in your video; you write '2' bottoms up