Geometrical Optics |
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| Law of reflection: | θ1 = θ2 |
| Law of refraction: | n1sinθ1 = n2sinθ2 |
| Total internal reflection: | sinθc = n2/n1 |
| Mirror equation: | 1/xo + 1/xi = 1/f, M = -xi/xo, f = R/2 |
| Lens equation: | 1/xo + 1/xi = 1/f, M =- xi/xo |
Wave Optics |
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| Double slit, diffraction grating (maxima): | d sinθ = mλ, m = 0, 1, 2, ... |
| Single slit, (minima): | w sinθ = mλ, m = 1, 2, ... |
| Resolving power: | θmin = 1.22 λ/D |
Photons and matter waves |
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| Photon energy: | Ephoton = hf = hc/λ |
| Photoelectric effect: | Eelectron = hf - Φ |
| Compton scattering: | Δλ = (λf - λi) = [h/(mec)](1 - cosθ) |
| De Broglie relations: | p = h/λ, E = hf |
| Matter waves: | λ = h/p = h/√(2mE) |
| Uncertainty principle: | Δx Δp ~ h/2π, Δt ΔE ~ h/2π |
Atoms |
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| Orbital angular momentum: | L2 = l(l+1)ħ2, l = 0, 1, 2,
... . Lz = mħ, m = -l, (-l + 1), ... , (l - 1), l |
| Electron spin: | Sz = msħ, ms = +½, -½ |
| Hydrogen-atom energies: | En = -13.6 eV/n2 |
| Hydrogen-atom energy eigenfunctions: | 4 quantum numbers: n, l, m, ms l < n |
| Atomic spectra: | hf = ∆E = Ehigh - Elow |
Nuclei |
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| Nuclear binding energy: |
B(Z,N) = c2(Z*mp + N*mn
- Mnuc(Z,N)) B(Z,N) = c2(Z*mH + N*mn - Matom(Z,N)) |
| Nuclear radius: | R = R0A1/3, R0 = 1.2*10-15 m. |
| Nuclear decay: | N(t) = N0exp(-λt) R(t) = R0exp(-λt) τ = 1/λ t½ = τ ln2 = ln2/λ. |
Constants and conversions |
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Elementary charge qe: Electron mass me: Proton mass mp: Neutron mass mn: Planck's constant h: Useful combination: Conversion: |
qe = 1.6 * 10-19 C me = 9.1 * 10-31 kg mp = 1.672 * 10-27 kg mn = 1.674 * 10-27 kg h = 6.63*10-34 Js = 4.14*10-15 eVs hc = 1240 eV nm 1 eV = 1.6*10-19 J |