Web of Connections in Ray Optics

Snell's Law (n_{1} sin θ_{1} = n_{2} sin θ_{2})
    │
    ├── θ_{2} = 90° ──→ Critical Angle (θ_c = arcsin(n_{2}/n_{1}))
    │                    │
    │                    └── TIR ──→ Optical Fibres, Diamonds, Mirages, Prisms
    │
    ├── Refraction at surface ──→ Apparent depth, Twinkling of stars
    │
    └── Lensmaker's Equation ──→ 1/f = (n−1)(1/$R_{1}$ − 1/$R_{2}$)
                                       │
                                       └── Thin Lens Formula ──→ 1/v − 1/u = 1/f
                                                                      │
                                                                      ├── Magnification (m = v/u)
                                                                      └── Power (P = 1/f)
                                                                              │
                                                                              └── Eye correction, Microscopes, Telescopes

Law of Reflection (∠i = ∠r)
    │
    └── Spherical Mirrors ──→ 1/v + 1/u = 1/f = 2/R
                                    │
                                    ├── f < 0: Concave (converging)
                                    └── f > 0: Convex (diverging)

Prism
    │
    ├── δ = (i + e) − A ──→ Minimum deviation (i = e, n = sin((A+δ_m)/2)/sin(A/2))
    └── Dispersion ──→ ω = (n_v − n_r)/(n_y − 1) ──→ Spectrum, Rainbow