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ALGEBRA 1 Version 2009
Revised and highly enlarged.
ALGEBRA 2
ALGEBRA 3
ALGEBRA 4
GEOMETRY 1
ELECTRICITY 1
ELECTRICITY 2
ELECTRICITY 1&2
OPTICS 1
OPTICS 2
MECHANICS 3
 
OPTICS 1
light, waves, photons, planets, vision...
Middle & High school 12-18 years


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   1. Light is emitted and absorbed by matter.
  •           1. Primary source of light
  •           2. Secondary source of light and light diffusion
  •           3. Light reflection
  •           4. White object and black object
  •           5. Light transmission
  •           6. Transparent, opaque and translucent substances
  •           7. Luminescence
   2. Light and our environment.
       3. Bohr's model of the hydrogen atom.
    •           1. Basic interaction of light and matter.
    •           2. Bohr's model of the hydrogen atom.
    •           3. Ground state of the hydrogen atom.
    •           4. E0, ionization energy of the hydrogen atom.
    •           5. Excited states n = 2 and n = 3.
    •           6. Generalization to a state n of Bohr's model.
    •           7. Computing and drawing the hydrogen atom energies.
       4. Emission of photons by the hydrogen atom - Lyman series.
    •           1. Photon emission occurs with conservation of energy.
    •           2. Photon energies in the first two transitions towards state m = 1.
    •           3. Determining and drawing the photon's spectrum in the Lyman series.
       5. Emission of photons by the hydrogen atom - Balmer series.
    •           1. Definition of the Balmer series.
    •           2. The 3®2 transition in the Balmer series.
    •           3. Determining and drawing the photon's spectrum in the Balmer series.
       6. Emission of photons by the hydrogen atom - Paschen series.
    •           1. Introduction to the Paschen series.
    •           2. Expression of Eg in the transitions n®3.
    •           3. Determining and drawing the photon's spectrum in the Paschen series.
       7. Name of electromagnetic radiations according to the photons energies they carry.
    •           1. Visible radiation.
    •           2. Infrared, visible and ultraviolet radiations.
    •           3. The spectrum of electromagnetic waves in terms of a photon's energy.
    •           4. Summary.
       8. Kinematics of the photon.
    •           1. A photon can only be described in the framework of relativity.
    •           2. Particle energy and momentum in relativity.
    •           3. Definition of a particle mass.
    •           4. Interpretation of Einstein's equation.
    •           5. A photon is a particle with zero mass.
    •           6. Definition of a particle velocity in relativity.
    •           7. Photon velocity and light velocity.
    •           8. Summary.
       9. To be familiar with the photon's kinematics.
         10. Light, umbra and penumbra.
      •           1. Rectilinear propagation of light.
      •           2. Umbra from a point light source.
      •           3. Umbra from an extended light source.
      •           4. Using light rays to explain an umbra.
      •           5. Defining the umbra of an extended light source.
      •           6. Observing the Umbra and penumbra of a ball lit by a light source.
      •           7. Reduced variables for a ball and a light source.
         11. Definition of the ellipse in polar coordinates. The planets of the solar system.
      •           1. Introduction.
      •           2. The sun and the planets.
      •           3. Definition and properties of the ellipse.
      •           4. Orbit of planet Icarus.
      •           5. Position of the second focal point, geometric definition of the ellipse.
      •           6. The second axis of symmetry of the ellipse.
      •           7. Summary.
      •           8. Dimensions of the planets and their orbits.
      •           9. Perihelion and aphelion of an elliptical orbit.
         12. Cones of umbra and penumbra of a planet.
      •           1. Length and half-angle of an umbra cone.
      •           2. Umbra cone of Earth.
      •           3. Umbra cone of the moon.
      •           4. Vertex position and half-angle of a penumbra cone.
         13. Earth and its natural satellite, the Moon.
      •           1. Motion of Earth around the Sun.
      •           2. Phases of the Moon.
      •           3. Lunar eclipse.
      •           4. Solar eclipse.
         14. Light rays, the Sun and the planets.
           15. The eye, the vision and the colors.
        •           1. Description of the eye.
        •           2. How the eye functions.
        •           3. Characteristics of a normal, farsighted or nearsighted eye.
        •           4. Composition of daylight.
        •           5. Colours by diffusion of an illuminated object.
        •           6. Colour by transmission.
        •           7. The trichromy.
        •           8. Synthesizing a colour.
        •           9. Perception du mouvement des formes et des couleurs.
           16. Vision and colours.
             17. Time description of a monochromatic wave.
          •           1. Wave amplitude and its representation.
          •           2. Measure of an angle in radians.
          •           3. Period T of a monochromatic wave.
          •           4. Definition of the frequency n of the wave.
          •           5. Planck's relation E = hn .
          •           6. Numerical correspondence between energy and frequency.
          •           7. Conventional limits of electromagnetic waves expressed in terms of frequency.
             18. Space-time description of a monochromatic wave.
          •           1. Space-time frame of reference.
          •           2. Angular frequency w and wave vector k of a plane monochromatic wave.
          •           3. Amplitude and phase of a monochromatic wave.
          •           4. Definition of the wavelength l.
          •           5. Summary.
          •           6. Plane wave propagation.
          •           7. Invariant form of the phase.
          •           8. Ray frequencies in the Balmer series.
             19. The photon and its associated electromagnetic wave.
          •           1. Wave and particle aspects of light.
          •           2. Wave-particle duality.
          •           3. Summary.
          •           4. Dispersion relation of an electromagnetic wave in vacuum.
          •           5. Phase velocity of an electromagnetic wave in vacuum.
          •           6. Relating the photon parameters to the associated plane monochromatic wave.
             20. Wavelength associated to a photon in function of its energy.
          •           1. Numerical correspondence between photon energy and its associated wavelength.
          •           2. The range of wavelengths in the visible light spectrum.
          •           3. Graph of the wavelength l as a function of the photon energy E.
          •           4. Photon energy emitted by a laboratory laser.
             21. Wavelengths of the hydrogen spectrum in Bohr's model.
          •           #g1. Energy of an emitted photon.#n
          •           #g2. Wavelength associated to a photon.#n
          •           #g3. Lyman series.#n
          •           #g4. Balmer series.#n
          •           #g5. Paschen series.#n