Geometrical Optics: A Sampler of the Geometrical Optics Topics

Contents:

  1. Introduction
  2. Derivation of the Laws of Reflection and Refraction
  3. The Invention of Eyeglasses
  4. Lenses, Curved Mirrors, and Image Formation
  5. Point Inversion
  6. Pinhole Projection
  7. Plane Reflection
  8. The Rayleigh Criterion
  9. Segmented Mirrors, The JWST, and Tiling

Sections:

  1. Introduction:

    As the title suggests, this file is sampler (or representative selection) of geometrical optics topics. It is NOT a full educational presentation, but rather a coherent presentation of interesting topics and results.

    Note:

    1. Geometrical optics treats light light rays: straight line beams of light stuff that travel from source to receiver.

    2. But to describe the reality of light at all and build simple optical devices one needs to include reflection and refraction at medium interfaces.

    3. Optical devices: e.g., binoculars, disco ball, eyeglasses, kaleidoscope, lens, magnifying glass (AKA magnifier), microscope, mirror, prism, spectroscope, stereoscope, telescope, etc.

    4. Physical optics treats light as electromagnetic waves which are derived from classical electromagnetism. Physical optics allows one to deal interference and diffraction and the creation and destruction of electromagnetic waves above the level of quantum mechanics and quantum optics.

  2. Derivation of the Laws of Reflection and Refraction:

    Formally, in geometrical optics one just takes the law of reflection (specular reflection off a smooth enough surface) and Snell's law (AKA law of refraction) as axioms.

    However, there are derivations. In fact, there are several of them of lesser or greater difficulty. Which derivations are valid? Yours truly believes they all are given their axioms as emergent emergent principles derived themselves from deeper physics, ultimately quantum electrodynamics (QED) which is way too deep for here.

    The derivations from Fermat's principle (in its modern Fermat's principle) is easy and instructive.

    We give it in Optics file: optics_geometrical_derivations.pdf.

  3. The Invention of Eyeglasses:

    Eyeglasses were invented circa 1290 in Europe (see Wikipedia: Glasses: Invention) and eyeglass makers were common by the 17th century when the telescope was invented Wikipedia: History of the telescope See the figure below (local link / general link: eyeglasses_history.html).

  4. Lenses, Curved Mirrors, and Image Formation:

    The figure below (local link / general link: optics_lens_curved_mirror.html) explicates lenses, curved mirrors, and image formation.

  5. Point Inversion:

    Point inversion is explicated in the figure below (local link / general link: optics_point_inversion.html).

  6. Pinhole Projection:

    Pinhole projection also gives an image with point inversion.

    If you don't have a guaranteed safe solar filter, you can use pinhole projection to look at the Sun at any time.

    Pinhole projection is explicated in the figure below (local link / general link: pinhole_projection.html).

  7. Plane Reflection:

    Plane reflection is illustrated and explicated in the figure below (local link / general link: optics_reflection_plane.html).

  8. The Rayleigh Criterion:

    The Rayleigh criterion is illustrated and explicated in the figure below (local link / general link: optics_rayleigh_criterion.html).

  9. Segmented Mirrors, The JWST, and Tiling:

    The figure below (local link / general link: telescope_segmented_mirror_4.html) describes segmented mirror telescopes, James Webb Space Telescope (JWST, 2021--2041?), and regular tiling polygons---what more could you ask for?

Local file: local link: optics_geometrical.html.
File: Optics file: optics_geometrical.html.