theorem 16.104 Snell's law of refraction

open in the book · parts/02-mathematical-methods/14-calculus-of-variations.tex:3290 · p. 667

Rests on

depends_on definition 16.103 Optical path length; Fermat's principle ¶
- depends_on equation 16.89 eq:calcvar-optical-length ¶
- depends_on lemma 16.100 The ray equation ¶
  - depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
  - depends_on equation 16.89 eq:calcvar-optical-length ¶ ↺
  - proves proof ch:14-calculus-of-variations@proof-47 ¶
depends_on lemma 7.33 Fermat: interior extremum ¶
- depends_on definition 7.26 Derivative of a function at a point ¶
  - depends_on definition 7.16 Limit ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on definition 7.9 Real function ¶ ↺
- depends_on proposition 7.18 Two-sided limit from one-sided limits ¶
  - depends_on definition 7.16 Limit ¶ ↺
  - depends_on equation 7.7 eq:ana-limit-left ¶
  - depends_on equation 7.5 eq:ana-limit-right ¶
  - proves proof ch:05-real-analysis@proof-6 ¶
- proves proof ch:05-real-analysis@proof-17 ¶
proves proof ch:14-calculus-of-variations@proof-49 ¶

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type	direction	node	provenance	where
`depends_on`	→	Optical path length; Fermat's principle	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3299
`depends_on`	→	Fermat: interior extremum	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3299
`proves`	←	ch:14-calculus-of-variations@proof-49	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3302