Physics 131

• Capacitive Reactance

  𝑋C = 1/𝜔𝐶
• Inductive Reactance

  𝑋𝐿 = 𝜔𝐿
• 𝑋𝐿 = 𝑋𝐶
• Phase angle between current and voltage

  tan−1 𝜙 = XL - XC/R
• Index of refraction of a medium

  c is the speed of light in the free space, v is the speed of light in the medium
• Snell's law of refraction

  n1 is the index of refraction of incident medium, n2 is the index of refraction of refracted medium
• Total Internal Reflection

  Occurs when light goes from a higher index medium n2 to a lower index medium n1 with incident angle larger than a critical angle 𝛉c: 𝜃𝑐 = sin−1 𝑛1/𝑛2
• Mirror Equation

  R = Radius of curvature
• Sign Conventions for Mirrors

  • Quantity, Symbol, In Front, In Back, Upright Image, Inverted Image, Object location p, +, -, Image location q, +, -, Focal length f, +, -, Image height hʹ, +, -, Magnification M, +, -
• Polarization of Light Waves

  Light intensity: I ~ E2 = E02cos2q (Malus' Law)
• Equation for thin lens

  1/f = (nl - n0)/n0 (1/R1 - 1/R2)
• Young's Double-Slit

  Constructive interference: 2nt = mλ, m = 0, 1, 2, …, Destructive interference: 2nt = (m + 1/2)λ, m = 0, 1, 2, …
• Check for other methods to create interference
• Interference in Thin Films (in air)

  2nt = mλ, m = 0, 1, 2, …, bright (constructive), 2nt = (m + 1/2)λ, m = 0, 1, 2, …, dark (destructive)
• Resolution

  a = slit size, D = Diameter of the mirror, L = Distance between two lenses, f0 = Focal length of the objective, fe = Focal length of the eyepiece
• Relativistic Velocity addition rule

  VAB = Speed of A measured from B, VAE = Speed of A measured from Earth, VBE = Speed of B measured from Earth
• Relativistic mass

  m/(1 - v2/c2) = γm = mr
• Temperature of Blackbody radiation


  (Plancks' constant)
• Photon energy

  n = 1, 2, 3, ..., f: frequency
• 1 eV = 1.602 × 10-19 J
• Bragg's law


  photon's scattering angle

  
• me = 9.1 × 10-31 kg = 0.511 MeV/c2, h = 4.135 × 10-15 eV.s, hc = 1240 eV.nm
• Wavelength of Hydrogen spectra

  m = 1, 2, 3, ..., n = m + 1, m + 2, ...
• Bohr model angular momentum


  L = mevr = nℏ, n = 1,2,3 ...
• Energy level and spectra for Hydrogen-like atom

  Z = Atomic number
• Electronic configuration of 29Cu atom
• What is the maximum number of electrons in a p state?
• Frame of reference

  A coordinate system used to describe a physical event
• According to this experiment, light could travel faster than light
• Maxwell's theory of electromagnetism says the speed of light is independent of motion

  
• Sound

  • Travels through a medium (air)
  • The medium serves as an absolute frame of reference (all speeds of sound waves are measured relative to the ambient air)
• Around 1895, physicists thought the same was true for light and called the medium "ether"
• The Michelson-Morley experiment found no interference fringe shift, concluding there is no ether
• Einstein's Principle of Relativity

  1. Laws of physics are the same in all inertial frames of reference (Inertial frame: where Newton's 1st law holds, no acceleration)

  2. The constancy of the vacuum speed of light
• If you were traveling in a spaceship at a speed relative to Earth and you fired a laser beam in the direction of the spaceship's motion, the light from the laser would not travel at a speed relative to Earth
• Simultaneity

  Two events that are simultaneous in one reference frame are in general not simultaneous in a second frame moving relative to the first
• Time dilation

  The time interval between two events measured by an observer who sees the events occur at the same position is shorter than the time interval measured by an observer in motion relative to the events
• Particle accelerators would not work without Special Relativity
• Atomic clocks sent on commercial flights around the world in 1971 demonstrated time dilation
• An astronaut traveling at a speed near the speed of light should choose to be paid according to the time elapsed on the ship's clock to maximize their paycheck