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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
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 D
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.