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Formulae and Constants: e = 1.60 x 10-19 Coulombs E = h f = hc / λ & momentum, p = h / λ 1 eV = 1.60 x 10-19 J h = Planck’s const = 6.63 x 10-34 J•s = 4.14 x 10-15 eV•s ____ hc = 1240 eV•nm 8 c = “speed of light” = 1 / √ (ε0 µ0) = 3 x 10 m/s c = λf Traveling wave equation: y(x,t) = A sin [k(x - vt)] = A sin (kx - ωt) = A sin [ (2π / λ) x - ( 2π / T) t ] where k = 2π / λ ω = 2π f = 2π / T v=ω/k Polarization • intensity of polarized light transmitted proportional to the amplitude squared: Malus’ Law I = I0 cos2θ • by reflection -- Brewster’s angle = polarizing angle -- tan θp = n2/n1 • by scattering For a crystal with thickness d, the phase difference between the 2 rays (ordinary and extraordinary) is Φ = [2π / λ0] * |n⊥ -n|| | * d Photoelectric Effect hf = φ + Ek or hc / λ = φ + eV0 or hc / λ = hc / λc + eV0 Blackbody Radiation: Wien displacement law λmax T = 2.880 x 106 nm•K Stefan-Boltzmann law energy / (time•area) = σ T 4 σ = 5.67 x 10 -8 W / (m2 K4) Bohr Model of Atom Allowed energy levels: En = -13.6 eV / n2 Energies of photons that can be emitted or absorbed = [exactly] | En1 -En2 | Reflection/refraction n=c/v λn = λ / n Snell’s Law: n1 sin θ1 = n2 sin θ2 For step-index fibers ___________ Numerical Aperture = N.A. = no sin θm = √ n12 -n22 ___________ Skip distance = Ls = n2 d / √ n12 -n22 # of modes = (1/2) [ π d (N.A.) / λ ] 2 in order to be single-mode, a fiber diameter d must be: d < 2.4 λ / π (N.A.) For fibers in general: Loss of power in dB = α L = 10 dB log10 (P1 / P2) where α is the attenuation coefficient Lenses/Mirrors Textbook sign conventions: [these assume light is coming from the left !] • if the object/image is to the left of the vertex (where lens/mirror crosses axis), its distance u/v is negative • radii of curvature follow the same rule as above, so diverging mirrors have positive f = focal lengths, but diverging lenses have negative focal lengths Object/image location Magnification Mirror Equations 1/u + 1/v = 2/r = 1/f m = hi / ho = - v / u Lens Equations - 1/u + 1/v = 1/f m = hi / ho = v / u For Mirrors: f = radius of curvature / 2 Lens Maker’s Equation: 1/f = [(n2 - n1 ) / n1] [ 1/r1 -1/r2 ] 3 standard rays for ray diagrams: • in thru focus, out parallel to axis • in parallel, out thru focus • in thru center, undeviated