RAY OPTICS AND OPTICAL INSTRUMENTS- 1-PAGE FORMULA SHEET

RAY OPTICS AND OPTICAL INSTRUMENTS - 1-PAGE FORMULA SHEET 1. Reflection Mirror formula: 1/f = 1/v + 1/u Magnification (mirror): m = h’/h = –v/u Radius–focal relation: f = R/2 Sign convention: • u always negative • f positive (concave), negative (convex) --- 2. Refraction (Snell’s Law) n₁ sin i = n₂ sin r Refractive index: n = c/v Optical path length: OPL = n × d --- 3. Refraction at Spherical Surface n₂/v – n₁/u = (n₂ – n₁)/R --- 4. Lens Formula 1/f = 1/v – 1/u Magnification (lens): m = v/u Focal length sign: • f greater than 0 (convex), f less than 0 (concave) --- 5. Power of Lens P = 1/f (f in metre) Equivalent power (thin lenses in contact): P_eq = P₁ + P₂ Equivalent focal length: 1/f_eq = 1/f₁ + 1/f₂ --- 6. Lateral Shift in Glass Slab δ = t × sin(i – r) / cos r --- 7. Total Internal Reflection Occurs when: • Light goes from denser → rarer • i greater than equal to C Critical angle: sin C = n₂/n₁ --- 8. Prism Formulae Prism deviation: δ = i₁ + i₂ – A Minimum deviation: n = sin((A + δₘ)/2) / sin(A/2) --- 9. Dispersion (Prism) Angular dispersion: Δθ = (n_v – n_r)A Dispersive power (ω): ω = (n_v – n_r)/(n – 1) --- 10. Optical Instruments (Ray Optics Part) Simple Microscope M = 1 + D/f Compound Microscope M = m_obj × m_eye m_obj = v/u m_eye = 1 + D/f_e Astronomical Telescope (Normal Adjustment) M = f_o / f_e Length L = f_o + f_e