ALGEBRA 1 Version 2009
Revised and highly enlarged.

Optics 2 . October 2010

We know that light is described as both waves and photons. What is more, several optical phenomena can be satisfactorily described with the help of optical geometry, which uses light rays. It is also essential that students know that light interacts with matter, via charged particles, principally electrons.

For this reason, teaching optics at the middle and high school levels is very difficult, which lead us to take a new and original approach to this subject.

In the title Optics 1 of this collection, we introduced light in terms of photons, emphasizing their interaction with the electric charges. We also introduced the wave-particle correspondence to link photon energy with the associated wave length and to study colors. The introduction of geometrical optics enabled us to explain the phenomena of umbra and penumbra, eclipses, etc.

The title Optics 2, which is aimed at high school as well as university students, begins by introducing the index n of a transparent medium related to the speed of light in the medium where it propagates. The phase of an electromagnetic wave, introduced in Optics 1, is covered once again. The continuity of the phase allows us to prove the laws of reflection and refraction, in particular the Snell-Descartes Law.

After studying the images formed by a plane mirror, we move on to the study of refraction, in particular the study of plane diopter, spherical diopter and thick lenses. Throughout this title, we use Newton's coordinates and formula XX'=ff', which is easy to memorize and use. This approach, which can be considered university-level, enabled us to show that the lens formulas result from the laws of refraction.

The study and graph of the Snell-Descartes Law lead to the introduction of the critical angle of refraction and its use in fiber optics. Two important applications are covered as courses and in the form of exercises :

  • The prism and its uses, in particular the measure of the refraction index n,
  • Reflections-refractions by a spherical drop of water and the calculations which give the positions of the radii of a single and double rainbow.

The applications of reflection are studied in three chapters devoted to concave, convex and parabolic mirrors, with the introduction of Fermat's Principle.

As an important example of the use of mirrors, we study the Hubble Space Telescope in the form of a problem where the mirror's are drawn to scale and the calculations based on Newton's relations. Extraordinary images taken by the telescope are presented with commentaries.

Chapter 14 covers the study of lenses, the definitions of linear and angular magnification. The association of two lenses is applied to vision correction. The microscope is studied in the form of a course and an exercise. An exercise is devoted to astronomical telescopes.

In the last chapter, we introduce the idea of light in the form of electromagnetic waves in a more precise manner and we show how their superposition leads to interference phenomena. An exercise is devoted to the drawing and calculation of interferences created by two Fresnel's mirrors.

Electricty 1. April 2009

This title is currently in the process of being translated and the English version
will be available shortly.


This title covers topics for both Middle and High Schools. A separate title, Electricty 1, is targeted at Middle school students; the complement, Electricity 2, is an independent title for High School students.

Electricity is a part of our environment; nevertheless, it is difficult to imagine that it is in our bodies and all the substances that surround us.

The first 3 paragraphs of chapter 1 are Middle School level. They introduce the hydrogen atom composed of two oppositely charged particles, the electron and the proton, bonded by the Coulomb attraction. Coulomb’s Law, which states that the magnitude of the electric force of two charges is inversely proportional to the square of the distance between them, is illustrated interactivelly : the student can vary the distance between the charges and observe the force of attraction. A calculation of a Coulommb force completes this paragraph.

The helium atom introduces a second electron in the electron cloud with a second proton and neutrons in the atom’s nucleus (neutral particles electrically composing the nucleaus).

The energy levels and the states of the hydrogen atom demand an understanding of Quantum Mechanics, which it is too early to cover, even in 12 th grade. However, these levels are described (without proof), in the framework of the Bohr model and are completed by the introduction of sub-levels represented graphically in the courses and exercises.

By using a model of an atom in which the electrons are independent in first approximation, subject to Coulomb attraction of the nucleus with an “effective” charge, we come down to the Bohr model which we complete by the quantum number l.

The Pauli exclusion principle and the two spin states of the electron enable construction of the eletronic configurations of elements, which are at the basis of spectroscopy and the whole chemistry.

The elements in the periodic table of elements are described, from hydrogen to neon then from sodium to argon.

An interactive and graphic exercise, corrected in the case of an error, allows the student to configure the elements up to Z=36 on the levels and sublevels.

Chapter 1 closes with the introduction of molecules and ionic and covalent bonds.