definition 16.103 Optical path length; Fermat's principle
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:3277
· p. 667
- ground object -- no derivation owed
Rests on
- 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 ¶
Supports
-
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
theorem 23.40
Eikonal and transport equations
¶
- depends_on proposition 23.41 Rays ¶ ↺
- depends_on theorem 16.104 Snell's law of refraction ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites
(history) |
→ | Œuvres de Fermat. Tome deuxième: Correspondance | derived | parts/02-mathematical-methods/14-calculus-of-variations.tex:3286 |
depends_on |
→ | eq:calcvar-optical-length | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3287 |
depends_on |
→ | The ray equation | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3287 |
depends_on |
← | Eikonal | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1248 |
depends_on |
← | Rays | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1313 |
depends_on |
← | Snell's law of refraction | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3299 |