equation 16.89 eq:calcvar-optical-length

open in the book · parts/02-mathematical-methods/14-calculus-of-variations.tex:3161

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depends_on definition 16.103 Optical path length; Fermat's principle ¶
- depends_on definition 23.39 Eikonal ¶
  - depends_on theorem 23.40 Eikonal and transport equations ¶
    - depends_on proposition 23.41 Rays ¶
    - depends_on remark 23.45 Why this is not an analogy ¶
- depends_on proposition 23.41 Rays ¶ ↺
- depends_on theorem 16.104 Snell's law of refraction ¶
depends_on example 16.110 Geodesics as extremals of proper time ¶
depends_on lemma 16.100 The ray equation ¶
- depends_on definition 16.103 Optical path length; Fermat's principle ¶ ↺
- depends_on proposition 23.41 Rays ¶ ↺
- depends_on theorem 16.101 Maupertuis–Euler–Jacobi principle ¶
  - depends_on proposition 23.10 The characteristic function is the abbreviated action ¶
    - depends_on remark 23.11 Whose principle, and where it fails ¶
  - depends_on remark 23.11 Whose principle, and where it fails ¶ ↺
depends_on proposition 16.105 The optical invariant in a stratified medium ¶

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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:3287
`depends_on`	←	Geodesics as extremals of proper time	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3500
`depends_on`	←	The ray equation	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3173
`depends_on`	←	The optical invariant in a stratified medium	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3341