Why does light slowing imply a bend? (Beyond the tank/car analogy)

A link to the full video is at the bottom of the screen.
Or, for reference: https://youtu.be/Cz4Q4QOuoo8

That video answers various viewer questions about the index of refraction.

Editing from long-form to short by Dawid Kołodziej
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https://www.youtube.com/watch?v=DWnb2UUlqd0