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Question about refractive and critical angles

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Hello, everyone!

I am really struggling with trying to understand the explanation given to this particular problem in the image I've attached. I more or less got the first half of it (although I am not sure what is meant by a ray "escaping"), but what really puzzles me is how a critical angle and a refractive angle can be complementary. Or does anyone have any alternative explanations to offer, perhaps?

Thank you so much in advance!

wtfphysics.png

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2EBt2Nc.jpg
"escape" refers to the ray that would refracts rather than total internally reflects, for incident angle from inside the fibre < c. c + r = 90° only in this setup of variables. Here r refers to refracted angle at ANOTHER normal, not the same one as the "escape" ray so the relationship holds only in context of this question.

Edited by kw0573

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