type: connection_note | topic: conceptual-connections

MEASUREMENT FOUNDATION
        │
   ┌────┴────┐
   │         │
Vernier   Screw Gauge
 (LC=0.02mm) (LC=0.01mm)
   │         │
   │    measure diameter for:
   │         ├─── Resistivity ρ = RA/L (need d → A = π$d^{2}$/4)
   │         └─── Young's modulus (need d for A in Y = FL/A$\Delta L$)
   │
   └─── Metre bridge uses balance principle → Wheatstone bridge
               │
               └─── Connects to Ohm's law (V-I graph, slope=R)
                          │
                          └─── Galvanometer (G) is bridge detector → half-deflection method

OPTICS CHAIN
   Concave mirror (1/v+1/u=1/f) ──── Cartesian signs ──── Convex lens (1/v-1/u=1/f)
         │                                                         │
   u-v method                                               u-v method
   (graph: 1/v vs 1/u)                               (graph: 1/v vs 1/u, intercepts=±1/f)
         │
   Prism: i-delta graph → minimum deviation → μ
         │
   Glass slab: μ = real/apparent depth (travelling microscope)

WAVES→SOUND
   Resonance tube → v = 2f(l_{2}-l_{1}) → speed of sound
         │
   Related: sound velocity v = √(γP/ρ) increases with temperature

SEMICONDUCTOR
   p-n junction I-V → Zener (reverse breakdown) → LED (emits light)
   Si threshold: 0.7V; Ge: 0.3V → wider band gap = higher threshold

Key Unifying Theme: All experiments use some form of balance or null method (Wheatstone bridge, resonance, equal moments) or graphical analysis (slope/intercept) to extract the physical quantity precisely.