ModernPhysics

• Scalar


  A quantity which is completely specified by a number and its unit (has magnitude, no direction, obey rules of ordinary algebra)
• Vector


  A quantity specified by both: magnitude and direction in space (obey rules of vector algebra)
• Scalar product (dot/inner product) of two vectors A and B

  Magnitude of A times the magnitude of B times the cosine of the angle α between these two vectors
• Vector product (cross/outer product) of two vectors A and B

  A × B = C, where |A × B| = |A||B|sinα, C ⊥ A, C ⊥ B
• Light is electromagnetic radiation that can be perceived by the human eye
• Light waves


  Part of the electromagnetic spectrum with wavelengths from about 400 nm (violet) to 700 nm (red)

  
• Poynting vector


  Describes the magnitude and direction of energy flow in an electromagnetic wave, S = (1/μ0)E × B
• Light travels along straight paths in a homogeneous medium
• Incident ray splits into reflected and refracted rays, all in the plane of incidence

  
• In an inhomogeneous medium, light rays are curved due to varying refractive index

  
• Mirages are caused by light rays bending upwards near a hot ground surface
• Interference


  Effect caused by overlapping identical waves, resulting in constructive or destructive interference
• Thin-film interference causes alternating light and dark bands

  
• Diffraction grating


  Optical component that splits and diffracts light into several beams

  
• Dispersion


  Angular separation per unit wavelength interval, D = dθ/dλ = m/dcosθ

  
• Resolving power


  Ability to distinguish closely spaced spectral lines, R = λ/Δλ = Nm

  
• Holography


  Technique to record both amplitude and phase of waves, producing 3D images

  
• Electromagnetic waves are transverse, with both electric and magnetic field vectors
• Holography


  Technique invented to preserve both the amplitudes and the phases of the wave fronts on a photographic plate called a hologram

  
• Photograph


  Projects a three-dimensional object onto two-dimensional format

  
• Hologram


  Preserves the information on the three-dimensional nature of the object
• Hologram formation


  1. Two coherent plane waves (reference wave and object wave) intersect on the plate

  2. They form an interference pattern of bright and dark fringes

  3. This pattern encodes the three-dimensional information of the object

  
• Hologram reconstruction


  1. Hologram is illuminated with the reference wave

  2. It reconstructs the original object wave

  3. Producing a three-dimensional image

  
• Polarization


  Electromagnetic waves are transverse waves because their electric field vector E and magnetic field vector B are perpendicular to the direction of propagation
• Unpolarized light


  No preferred plane containing the E vector
• Linearly polarized light


  Electric vector E remains in only one fixed direction

  
• Circularly polarized light


  Light is composed of two plane waves of the same amplitudes and their phase difference is equal to π/2

  
• Law of Malus


  1. Only the y component of E is transmitted through a polarizing sheet

  2. Transmitted light amplitude is E*cosθ

  3. Transmitted light intensity is E^2*cos^2θ

  
• Brewster's angle


  Particular angle of incidence at which the reflection coefficient for the polarization component in the plane is equal to zero
• At Brewster's angle, the component with polarization parallel to the plane of incidence is entirely refracted, whereas the perpendicular component is partially reflected and partially refracted
• Wave-particle duality of light

  Light is at the same time a wave and a stream of particles, called photons
• Wave nature of light

  • Interference phenomenon
  • Diffraction phenomenon

  
• Corpuscular nature of light

  • Bremsstrahlung
  • Einstein's photon theory
  • Bothe experiment
  • Compton effect
  • Photoelectric effect

  
• Stefan-Boltzmann law


  Total radiated power per unit area of a black body is proportional to T^4
• Wien displacement law


  Wavelength of maximum spectral radiance is inversely proportional to temperature

  
• Photoelectric effect


  1. Metal under influence of light emits electrons

  2. Electrons are pulled to a positive electrode

  3. Saturation voltage is reached when all electrons are collected

  4. Stopping voltage is reached when current stops
• Einstein's photon concept of photoelectric effect

  hv = A + Emax, where hv is photon energy, A is work function, and Emax is maximum electron kinetic energy
• If hv < A, no photoelectrons are emitted regardless of light intensity
• Increasing light intensity increases the photoelectric current
• De Broglie hypothesis


  Particles, such as electrons, have wave-like properties with wavelength λ = h/p