pathLength2
plain-language theorem explainer
Defines the Euclidean path length from source through the second slit (offset +d/2) to screen point y. Physicists reconstructing double-slit fringes from Recognition Science phase accumulation cite this geometric primitive. It is a direct square-root expression using the setup parameters L and d.
Claim. The path length through the second slit to screen coordinate $y$ equals $l_2(y) = L^2 + (y + d/2)^2$ under square root, where $d > 0$ is slit separation and $L > 0$ is distance from slits to screen.
background
DoubleSlitSetup is the parameter record holding slit separation $d$, screen distance $L$, and wavelength, each required positive. The module derives the double-slit pattern from 8-tick phase accumulation: two paths collect phases whose difference produces intensity $2 + 2 cos(Δφ)$ at the screen. Upstream DoubleSlitSetup supplies the concrete values of $d$ and $L$ that enter the distance formula.
proof idea
One-line definition that applies the Euclidean distance formula in the plane: vertical leg $L$, horizontal leg $y + d/2$.
why it matters
Supplies the second path length required by the amplitude definition that sums the two complex exponentials. This geometric step precedes phase extraction and intensity oscillation inside the QF-012 derivation of interference from the 8-tick structure. It closes the classical path geometry before Recognition Science phase rules are applied.
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