A lot of optical illusions can be explained by Fermat's principle of least time, but why does light obey it? On a fundamental level, it all comes down to quantum mechanics, specifically quantum optics, where we use the famous "Feynman path integral formulation" to explain light through photons.
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VIDEO ANNOTATIONS/CARDS

How Fast Is Light?
https://youtu.be/a9T26ItpcDA

Lagrangian Mechanics:
https://youtu.be/MIBfKJHMWHU

You Don't Know How Mirrors Work:
https://youtu.be/rYLzxcU6ROM
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OTHER SOURCES

https://www.feynmanlectures.caltech.edu/I_26.html
https://www.feynmanlectures.caltech.edu/I_27.html
https://www.feynmanlectures.caltech.edu/I_31.html
http://www.vega.org.uk/video/subseries/8
https://www.physicsclassroom.com/Class/refrn/u14l1b.cfm
Optics by Hecht
https://www.engineeringtoolbox.com/refractive-index-d_1264.html
https://www.etymonline.com/word/refraction
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LINKS TO COMMENTS

https://www.youtube.com/watch?v=1n_otIs6z6E&lc=UgzJ-NZ6tSFKnQEsiVB4AaABAg
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IMAGE CREDITS

Black Hole Visualization:
https://www.nasa.gov/feature/goddard/2019/nasa-visualization-shows-a-black-hole-s-warped-world