{"query": "Optics — how light bends, focuses, and slows", "count": 20, "results": [{"id": "card_floor_optics", "title": "Optics — how light bends, focuses, and slows", "shelf": "codex", "surface": "secular", "snippet": "Light is a Maxwell wave that slows in matter (v = c/n) and bends at boundaries (refraction); lenses focus it by the thin-lens equation; and a beam is also a stream of photons. Three pillars rest on Ma", "authority_tier": "engine_derived", "source": "Narrow Highway — optics", "readable": false, "generated": false}, {"id": "card_theory_vsepr_theory", "title": "VSEPR theory (molecular geometry)", "shelf": "theories", "surface": "secular", "snippet": "VSEPR theory (molecular geometry) — an engine domain that can touch it: molecular_geometry. Calibration: seals — shapes and bond angles predict directly. Valence Shell Electron Pair Repulsion: electro", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_59d0a5126171", "title": "Psalm 11 — Psalm 11", "shelf": "codex", "surface": "witness", "snippet": "<<For the Chief Musician. By David.>> In Yahweh, I take refuge. How can you say to my soul, \"Flee as a bird to your mountain!\" For, behold, the wicked bend their bows. They set their arrows on the str", "authority_tier": "scripture", "source": "Psalm 11", "readable": false, "generated": false}, {"id": "card_nav_orient_map", "title": "Orienting the map to the ground", "shelf": "navigation", "surface": "secular", "snippet": "Orient the map so its top (north) points to real north — then everything on the paper lines up with the world in front of you. Lay the compass on the map with its edge along a north-south grid line, t", "authority_tier": "reference", "source": "U.S. Army FM 3-25.26 — Map Reading and Land Navigation (public domain)", "readable": false, "generated": false}, {"id": "card_sys_thermal", "title": "Thermal systems", "shelf": "systems", "surface": "secular", "snippet": "Effort = temperature, flow = heat flow. Thermal resistance (Fourier: q = ΔT/R), thermal capacitance (a body's heat storage); no true thermal inductor (heat has no inertia) — the one place the analogy ", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_alm_located_relativistic_doppler_reciprocal", "title": "Almanac: Relativistic Doppler: approaching light doubles, receding halves, the product is one", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Move toward a light source and its frequency rises (blueshift); move away and it falls (redshift). Relativity sets the exact factor at sqrt((1+b)/(1-b)) with b=v/c. The mathematics verifie", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_n_a7ae37960cae", "title": "FM broadcast (VHF) — three-meter waves, line of sight", "shelf": "science", "surface": "secular", "snippet": "88–108 MHz; sealed: the 100 MHz wave is 2.99 m, and its quarter-wave whip is 74 cm —\nthe length of a car antenna, derived: https://narrowhighway.com/s/d6211f4efb2518c6de145decf57f27b131a01c24ce7841853", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_works_snell", "title": "Light bends: Snell's law at a glass surface", "shelf": "the-works", "surface": "secular", "snippet": "Passing from air into glass (n = 1.5) at 30°, a ray refracts to 19.47° — n₁ sin θ₁ = n₂ sin θ₂. The same law bends every lens and every rainbow.  Worked & sealed by the engine — sin θ₂ = (1·sin30)/1.5", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_src_etym_ply", "title": "ply", "shelf": "etymology", "surface": "secular", "snippet": "ply: etymology (Webster 1913) — v. t.: [OE. plien, F. plier to fold, to bend, fr. L. plicare; akin to Gr. flechten. Cf. Apply, Complex, Display, Duplicity, Employ, Exploit, Implicate, Plait, Pliant, F", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_opt_refraction", "title": "Refraction — light slows and bends", "shelf": "codex", "surface": "secular", "snippet": "Light travels at c/n in a medium (2.0e8 m/s in glass, sealed); the slowing bends it at a boundary (Snell), splits a prism (n varies with colour), and traps light in a fibre at the critical angle. Rest", "authority_tier": "engine_derived", "source": "Narrow Highway — optics", "readable": false, "generated": false}, {"id": "card_src_etym_bend", "title": "bend", "shelf": "etymology", "surface": "secular", "snippet": "bend: etymology (Webster 1913) — v. t.: [AS. bendan to bend, fr. bend a band, bond, fr. bindan to bind. See Bind, v. t., and cf. 3d & 4th Bend.]; n.: [See Bend, v. t., and cf. Bent, n.]; n.: [AS. bend", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_book_59740", "title": "Lost Mine Trail, Big Bend National Park, Texas — Anonymous", "shelf": "gutenberg", "surface": "secular", "snippet": "Lost Mine Trail, Big Bend National Park, Texas, by Anonymous. Subjects: Big Bend National Park (Tex.). Read the full text (public domain): https://www.gutenberg.org/ebooks/59740", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_book_51817", "title": "Big Bend National Park, Texas — United States. National Park Service. Division of Publications", "shelf": "gutenberg", "surface": "secular", "snippet": "Big Bend National Park, Texas, by United States. National Park Service. Division of Publications. Subjects: Big Bend National Park (Tex.). Read the full text (public domain): https://www.gutenberg.org", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_book_62658", "title": "Big Bend National Park: Land of Dramatic Contrasts and Scenic Grandeur — W. Ray Scott", "shelf": "gutenberg", "surface": "secular", "snippet": "Big Bend National Park: Land of Dramatic Contrasts and Scenic Grandeur, by W. Ray Scott. Subjects: Big Bend National Park (Tex.). Read the full text (public domain): https://www.gutenberg.org/ebooks/6", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_pron_bends", "title": "bends", "shelf": "pronunciation", "surface": "secular", "snippet": "bends: pronounced (ARPABET) B EH1 N D Z. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_pron_bend", "title": "bend", "shelf": "pronunciation", "surface": "secular", "snippet": "bend: pronounced (ARPABET) B EH1 N D. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_etym_bow", "title": "bow", "shelf": "etymology", "surface": "secular", "snippet": "bow: etymology (Webster 1913) — v. t.: [OE. bowen, bogen, bugen, AS. bugan (generally v.i.); akin to D. buigen, OHG. biogan, G. biegen, beugen, Icel. boginn bent, beygja to bend, Sw. böja, Dan. böie, ", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_principle_carl_von_clausewitz_9d420c0486", "title": "Carl von Clausewitz: To avoid any very great bends, more direct roads, even if smaller, must be chosen, for a line of retreat which", "shelf": "strategy", "surface": "secular", "snippet": "To avoid any very great bends, more direct roads, even if smaller, must be chosen, for a line of retreat which deviates much from a direct line is always perilous.", "authority_tier": "primary", "source": "Carl von Clausewitz, On War (tr. J. J. Graham) (1873) — Project Gutenberg #1946, public domain", "readable": true, "generated": false}, {"id": "card_src_etym_sinuate", "title": "sinuate", "shelf": "etymology", "surface": "secular", "snippet": "sinuate: etymology (Webster 1913) — a.: [L. sinuatus, p. p. of sinuare to wind, bend, fr. sinus a bend.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_etym_bought", "title": "bought", "shelf": "etymology", "surface": "secular", "snippet": "bought: etymology (Webster 1913) — n.: [Cf. Dan. bugt bend, turning, Icel. bug. Cf. Bight, Bout, and see Bow to bend.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_floor_optics"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}