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ALGEBRA 1 Version 2009
Revised and highly enlarged.
Reflection, refraction, rainbows, mirrors, prisms, lenses... Microscopes, telescopes, interferences...
High school & College 15-18 years

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   1. Index of a transparent medium. Phase velocity.
  •           1. Review of the phase of progressive monochromatic waves.
  •           2. Definition of phase velocity.
  •           3. Review of the relation between w and k in vacuum.
  •           4. Propagation of light in a transparent medium. Definition of index n.
  •           5. Phase velocity of light in a medium of index n.
  •           6. Indices of several substances in our environment.
  •           7. Refringence and dispersion of three grades of glass.
  •           8. Velocity of light in water and glass.
  •           9. Velocity of light in air, compared to c, velocity in vacuum.
   2. Reflection and refraction of light: Snell-Descartes Law. Critical angle.
  •           1. An experiment which displays reflection and refraction.
  •           2. Choice of reference frame. Wave vectors and pulsations.
  •           3. Linking the incident and reflected wave phases.
  •           4. Linking the incident and transmitted wave phases.
  •           5. Knowledge Sheet. Laws of reflection and refraction.
  •           6. Reflection and transmission in terms of photons.
  •           7. Normal incidence.
  •           8. Grazing incidence, critical angle.
   3. Reflection on a plane mirror: formation of images.
  •           1. Laws of reflection applied to a plane mirror.
  •           2. Path of rays emitted by a point light source.
  •           3. Image of a point in a plane mirror.
  •           4. Image of a polar vector.
  •           5. Image of an oriented circular loop.
  •           6. Image of a word in a mirror. Finding the error.
  •           7. Rotation of the reflected ray when we turn the mirror plane.
  •           8. Knowledge sheet.
   4. Images formed by refraction. Object and image focal points. Spherical diopters and lenses.
  •           1. Image of a coin in a pool.
  •           2. Image of a coin in a spherical aquarium.
  •           3. Spherical diopters in monochromatic light. Conjugation formula and focal points.
  •           4. Conjugation formula with origins at the focii: Newton's formula.
  •           5. Conjugate planes, focal planes. Definition and formulas of magnification.
  •           6. Image formed by two coaxial diopters. Conjugation relation and focal points of a thick lens.
  •           7. Magnification of a thick lens, focal lengths, unit planes.
  •           8. Knowledge sheet 1: main properties of thick lenses.
  •           9. Knowledge sheet 2: properties of thin lenses according to the index n and the curvature radii.
  •           10. Focal lengths of thin lenses given the index and radii of curvature.
   5. Properties of the laws of refraction, critical angle. Application to fibre optics.
  •           1. Study and graph of the Snell-Descartes law. Critical angle of refraction.
  •           2. Time reversal invariance: principle of the inverse return of light.
  •           3. Refraction in a less refractive medium. Critical angle.
  •           4. Fiber optics.
  •           5. A cylindrical bar illuminated by a laser beam.
   6. Dispersion of white light by a block of semi-cylindrical glass.
  •           1. Variation of index n of glass with the wavelength.
  •           2. Refraction by the plane surface then by the cylindrical surface.
  •           3. Incident white light on the plane surface.
  •           4. Incident white light on the cylindrical surface.
   7. Deviation of monochromatic light by a prism. Measure of index n.
  •           1. Description and characteristics of optical prism.
  •           2. Knowledge Sheet.
  •           3. Basic equations of the refraction by a prism.
  •           4. Refraction of a ray of monochromatic light.
  •           5. Searching for minimum deviation. Angles corresponding to this deviation.
  •           6. Measure of index n of a prism using the minimum deviation.
  •           7. Critical angle of incidence on a prism.
   8. Applications with prisms and total reflection. Refraction by a spherical drop.
  •           1. To change the direction of light by a quarter-turn.
  •           2. To change the direction of light by a half-turn.
  •           3. Moving a light ray without changing its direction: principle of a periscope.
  •           4. Refraction of light by a pane of glass.
  •           5. Deviation of light by a spherical drop of water. The origin of rainbows.
   9. Dispersion of light by a prism and by a drop of water : rainbow.
  •           1. Dispersion of white light by a prism.
  •           2. Incident monochromatic light on a spherical drop of water. Angular relations.
  •           3. Incident monochromatic light on a spherical drop of water. Angular deviation.
  •           4. Determining the maximum deviation analytically.
  •           5. Concentration of rays in the neighbourhood of Dm.
  •           6. How do arcs of a rainbow form ?
  •           7. Angular openings of the colored arcs of a rainbow.
  •           8. Double rainbow. Secondary rainbow.
   10. Concave spherical mirrors. Focusing at the Gaussian approximation. Images.
  •           1. Concave and convex spherical mirrors.
  •           2. Reflection of a light ray parallel to the mirror's axis.
  •           3. Observing the focalisation of rays parallel to the mirror's axis. Focal length.
  •           4. Collimate a beam of light parallel to the mirror's axis.
  •           5. Construction of the image of a point in a mirror.
  •           6. Image of a candle placed above the focal point F.
  •           7. Virtual image of a candle placed between the focal point and the mirror.
   11. Concave spherical mirrors: Newton's conjugation relation and magnification.
  •           1. Relations between the position of the object and the image.
  •           2. Conjugation relation: Newton's formula.
  •           4. Comparison of the conjugation formulas of mirrors and lenses.
  •           5. A ray that reflects symmetrically with respect to the mirror's axis.
  •           6. Study and graph of Newton's conjugation relation.
  •           7. Use of the conjugation graph to determine the position of the image and the magnification.
  •           8. Position of the image and magnification in a concave spherical mirror.
   12. Convex spherical mirrors. Images, conjugation relation, magnification.
  •           1. Reflection of a light ray parallel to the axis of a convex mirror.
  •           2. Observe the reflected ray when varying the incident parallel ray: focal point of the convex mirror.
  •           3. Image of a candle in a convex mirror.
  •           4. Magnification of a convex mirror. Newton's conjugation relation.
  •           5. Study and graph of Newton's conjugation relation.
  •           6. Position of the image and magnification in a convex spherical mirror.
  •           7. Focal length of a spherical mirror from geometric dimensions.
   13. Parabolic mirror. Fermat's principle. Optics and images of the Hubble telescope.
  •           1. Limits of the spherical mirror. Parabolic mirror.
  •           2. Characteristics and equation of a parabolic mirror.
  •           3. Geometric property of the parabola.
  •           4. Comparisons of spherical and parabolic mirrors with the same focal length.
  •           5. Focalization of the parabolic mirror. Fermat's principle.
  •           6. Image of an object at infinity: relation between the apparent angle and the image's diameter.
  •           7. Components and optical properties of telescopes. Cassegrain assembly.
  •           8. Description and principal characteristics of the Hubble space telescope.
  •           9. Image and magnification of an object by the Hubble telescope.
  •           10. Images captured by the Hubble telescope.
   14. Focal points of a lens. Image formation. Conjugation formula. Magnification.
  •           1. Description and classification of lenses. Examples.
  •           2. Discovery of the focal image point of a convergent lens in the open air, from the image of the sun.
  •           3. Observation, in a laboratory, of the focal image point and focal image plane of a convergent lens.
  •           4. Object focal point and object focal plane of a convergent lens. Production of a parallel beam.
  •           5. How does the magnifier give an enlarged image of an object?
  •           6. Magnification and magnifying power of a magnifier.
  •           7. A look back at Newton's conjugation formula and magnification.
  •           8. Image of far away object: relation between the apparent angle and the diameter of the image.
  •           9. Image focal point and focal plane, object focal point and focal plane of a divergent lens.
  •           10. Graph of the conjugation formula. Positions and sizes of images.
  •           11. Use the conjugation relation to determine the positions of the images and the magnifications.
   15. Two lenses used in association. Microscopes, telescopes, normal and myopic eyes.
  •           1. To be aquainted with the basic properties of lenses.
  •           2. Comparison of images given by a convergent lens and a divergent lens.
  •           3. Model of the eye' crystalline using a convergent lens: normal eye and myopic eye.
  •           4. Newton's conjugation relation for two thin lenses used in association. Magnifying power.
  •           5. Knowledge sheet. Formulas for two lenses in association. Thin lenses placed side by side.
  •           6. The microscope: objective, eyepiece, angular magnification.
  •           7. Eyepiece circle. Power of the microscope, resolving power.
  •           8. Study of a high magnifying power microscope.
  •           9. The main elements of an optical microscope.
  •           10. Astronomical telescope and refracting telescope.
   16. Light as electromagnetic waves. Interferences: Fresnel's mirrors.
  •           1. Progressive monochromatic electromagnetic plane wave. Phase and polarization.
  •           2. Young's double-slit experiment. Interference of two coherent monochromatic waves.
  •           3. Expression of the phase for two point sources. Interference fringes.
  •           4. Creating interference with Fresnel's mirrors.