Reflection

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Discussion

geometric optics

Light travels in straight lines with relatively little diffraction.

Pierre de Fermat (1601-1665) France, "principle of least time". Pierre Louis Moreau de Maupertuis (1698-1759) "principle of least action" in 1747 or 1750? Maupertuis hoped that the principle might unify the laws of physics and support his proof of the existence of God.

The wisdom of Beekman. "We don't see things. We see light bouncing off things."

reflection

A plane mirror produces only one inversion: front-to-back. This is called a perverted image.

Summary

• Optics is the study of the nature and behavior of light.
  It can be divided into subdisciplines based on the type of model used to describe light.
  • In physical optics, light is assumed to behave like a classical wave.
  • In quantum optics, light is assumed to have both wave and particle properties.
    • Particles of light are called photons.
  • In geometric optics, light is assumed to travel in a definite direction with relatively little diffraction.
    • This behavior is known as rectilinear propagation.
    • The path of propagation of a light wave is a geometric ray.
      • The rays of geometric optics …
        • are perpendicular to the wave fronts of physical optics.
        • indicate the most probable path of the photons of quantum optics.
      • A ray is the path of least action connecting two points in space and is also …
        • the path of least time (the quickest path)
        • the path of least distance (the shortest path)
        • unique and therefore reversible
          • The principle of reversibility states that light will follow exactly the same path if its direction of travel is reversed.
      • Rays are …
        • straight lines in empty euclidean space
        • geodesics in general relativistic space-time
      • The eye can see something only if a ray from the object reaches the eye.
• Interface
  • An interface is the boundary between …
    • two different media.
    • two regions of a medium with different characteristics such as …
      • density (which is often related to temperature)
      • concentration of solute (salinity, for example)
      • mechanical stress
  • When an incident ray meets an interface it will be partially
    • reflected
      • Reflected rays obey the law of reflection described in this section of this book.
    • transmitted
      • Transmitted rays obey Snell's law, which is described in the next section of this book.
    • absorbed
      • Absorbed rays obey the law of conservation of energy. (The energy of the ray is not destroyed, but changes form.)
  • Angles in geometric optics are measured with respect to a line normal to the interface.
    • The angle of incidence is the angle between the incident ray and the normal.
    • The angle of reflection is the angle between the reflected ray and the normal.
    • The angle of refraction is the angle between the transmitted ray and the normal.
• Reflection
  • Law of reflection: The angle of incidence equals the angle of reflection.
    • The law of reflection can be derived from the principle of least action.

Problems

practice

1. Write something.
   • Answer it.
2. Write something else.
   • Answer it.
3. Write something different.
   • Answer it.
4. Write something completely different.
   • Answer it.

numerical

1. problems

Resources

• general
  • The Mechanical Universe and Beyond (video on demand, login required)
    • Optics, Many properties of light are properties of waves, including reflection, refraction, and diffraction.

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