Mirror formula: 1/v + 1/u = 1/f = 2/R. Sign convention: distances measured from pole. Distances in direction of incident light = positive.
Magnification: m = -v/u = h'/h. m negative → inverted image. m positive → erect image. |m| > 1 → magnified.
Concave mirror uses: Real, inverted image (object beyond F) — cameras, projectors. Virtual, erect, magnified (object between F and P) — shaving/make-up mirror. Also used in headlights (parallel beam → F to parallel).
Snell's law: n₁ sin θ₁ = n₂ sin θ₂. n = c/v. Denser medium → slower speed, larger n, smaller angle.
Total Internal Reflection (TIR): When light goes from denser to rarer medium at angle > critical angle θ_c. sin θ_c = n₂/n₁ = 1/n (for n₂ = air). Applications: optical fibre, prism binoculars, diamond brilliance.
Lens formula: 1/v - 1/u = 1/f. Lens maker's equation: 1/f = (n-1)(1/R₁ - 1/R₂). Magnification: m = v/u.
Power of lens: P = 1/f (in metres) in Dioptres (D). Concave lens: f negative, P negative. Convex: f positive, P positive. Combination: P_total = P₁ + P₂ + P₃.
Path difference: Δ = d sin θ ≈ dy/D (for small θ). Bright fringe: Δ = nλ. Dark fringe: Δ = (2n-1)λ/2.
Fringe width: β = λD/d. β increases when: D increases (screen farther), λ increases (red > violet), d decreases (slits closer).
Central maxima: n=0, zero path difference, all wavelengths reinforce → white central bright fringe in white light.
Intensity: I = 4I₀cos²(δ/2) where δ is phase difference. Max intensity = 4I₀ (constructive). Min intensity = 0 (destructive, if I₁ = I₂ = I₀).
Single slit diffraction: First minimum at a sin θ = λ, or θ ≈ λ/a. Central maximum width = 2λD/a. Central maximum is twice as wide as secondary maxima.
Resolving power: Rayleigh criterion: θ_min = 1.22λ/D. Larger lens diameter → smaller θ_min → better resolution. Microscope uses shorter λ (electron microscope) for better resolution.
Polarisation: Only transverse waves can be polarised. Light is a transverse EM wave → can be polarised. Sound is longitudinal → cannot be polarised.
Malus's law: I = I₀cos²θ. θ = angle between polaroid axis and plane of polarised light. At θ = 90°, I = 0 (complete extinction). At θ = 0°, I = I₀ (full transmission).
Brewster's angle: tan θ_B = n. At Brewster's angle, reflected light is completely polarised (parallel to surface). Refracted light is partially polarised.
Lens: 1/v - 1/u = 1/f
Mirror m = -v/u
Lens m = v/u
Power P = 1/f(m) in Dioptre
Combination: P = P₁+P₂
Path diff. Δ = dy/D
Bright: Δ = nλ
Dark: Δ = (2n-1)λ/2
Max intensity: 4I₀ (if I₁=I₂=I₀)
Min intensity: 0
Diamond (n≈2.42): θ_c ≈ 24°
Glass (n≈1.5): θ_c ≈ 42°
Optical fibre: TIR principle
Condition: denser → rarer + θ > θ_c
Brewster's angle: tan θ_B = n
At Brewster's: reflected = plane polarised
Unpolarised → polaroid: I = I₀/2
Sound: cannot be polarised (longitudinal)
Mirror/lens formula: 1 Q/year
TIR/critical angle: 1 Q/year
Polarisation/Malus law: 1 Q/year
Expected: Combination of lenses
Watch: Polaroid intensity calculation