# Geometrical optics and mechanics of a material point

## Presentation

Program (detailed contents):

Optics :

Nature of the light. Colors. Laws and approximation of

Optics. Dioptres, lenses, mirrors. Transverse and angular magnifications. Combination of elements to realize optical instruments. Measurement uncertainty and metrology.

Mechanics :

Kinematic: concepts of trajectory and inertial reference frame. Expression of position, velocity and acceleration vectors in Cartesian, cylindrical and Frenet coordinate systems.

-Dynamics: The usual forces, the three Newton laws of dynamic, the theorem of angular momentum. Determination of the mechanical equations of a problem and solve them mathematically.

-Energy: Work of a force and potential energy, kinetic energy theorem and the principle of conservation of mechanical energy.

-Relativity: Relative movement and change of inertial frame.

Organization:

- Optics: 16 project sessions, 2 lectures, 5 lab work session.

- Mechanics: 7 lectures, 13 tutorials, 1 project session.

Main difficulties for students:

- Notation for differentiation and differential equation solving. -   Trigonometry and manipulation of coordinate systems.

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

Optics :

Gauss approximation, nature of objects and images, properties of single optical elements (dioptres, mirrors, lenses) and optical instruments made up of several single elements.

Mechanics :

Kinematics of a material point, the three Newton laws of dynamic, the theorem of kinetic energy, the concepts of relativity and inertial forces.

The student will be able to:

Optics :

Manipulate optical elements to constitute an optical instrument. Realize geometric constructions of images through several optical elements. Use formula to calculate the size and positions of images.

Mechanics :

Describe the movement (position, speed, acceleration) of a material point in different coordinate systems based on a given reference frame. Determine the external forces experienced by a material point and know the expression of the usual mechanical forces (gravity, electromagnetic, restoring force of a spring, reaction of a support and strength of friction, inertial pseudo-forces). Determine the trajectory or timetables equations of a material point from the fundamental principle of dynamics, the theorem of angular momentum and / or kinetic energy theorem.

## Needed prerequisite

-Notation for differentiation.

- trigonometry

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...