Mathematics 309 - Topics in geometry - Spring 2004

The mathematics of light

  • Course outline
  • Topics outline
    • Simple refraction
      • Snell's law
      • Fermat's principle
      • Huyghens' observation
    • Ray tracing
      • The general situation
      • Spherical lens surfaces
      • Gaussian optics
      • Rainbows
    • The linear theory
      • Transfer matrices
      • The principal planes
      • Focal length
      • Properties of lens systems
    • Aberrations
      • Optical length
  • First assignment (due January 14)
  • Second assignment (due January 21)
    This assignment will require computer work. Class on Friday, January 16, and on Monday, January 19, will be held in the computer lab Mathematics 202, for an introduction to the course spreadsheet. Starting Wednesday, January 21, class will be held in Buchanan D238 (right next to the current room Buchanan 244) in order to have available the overhead LCD projector in that room.
  • Third assignment (due February 4)
  • Fourth assignment (due February 25)
  • Fourth assignment solutions
  • Recall - mid-term examination Friday, February 27
  • Fifth assignment (due Wednesday, March 10)
  • Fifth assignment solutions
  • If you log in to the spreadsheet with group m309, when you go to load files you will see in the file list a number of files answer.m309.*. These are in effect answers to the assignments.
  • Course notes from last year
  • A major component of the course will be student class presentations. It might not be feasible for every one to give one, and time slots will be awarded on a first come, first serve basis. Thos who don't make the cut will have to do either a web project or a written essay. The subject of every project must be agreed on by me and every student before approval. Topics may not be duplicated. Joint presentations are not impossible, ut require extra consieration. Before giving your presentation, be sure to read my notes on student class presentations.
  • References
    • A copy of Geometric optics by J. Warren Blaker, a text book mostly concerned the linear theory, has been put on 2 hour reserve in the Mathematics Library. It is useful but not generally very exciting. The most interesting part is Chapter 7 on aberrations (i.e. deviations from linearity).
    • Also a copy of Chapters 2 and 3 Introduction to matrix methods in optics by A. Gerrard and J. M. Burch.
  • Student presentations
    • March 12 (F) -
    • March 15 (M) - Saleema Amershi [ Light issues in computer graphics ]
    • March 17 (W) - Trevor Kinsey [ Atmospheric refraction ]
      • Presentation [ .ppt ] [ .pdf ]
      • Notes and references [ .doc ]
      • Calculation spreadsheet [ .xls ]
    • March 19 (F) - Jeremy Janzen [ Aberrations - curvature of field ]
    • March 22 (M) - Kevin Greene [ Huyghens' principle ]
    • March 24 (W) - Asha Padmanabhan and Katrina Brubacher [ Rainbows and supernumerary bows ]
      • Presentation [ .ppt ]
    • March 26 (F) - Ryan Leslie [ Sky colours ]
    • March 29 (M) - Tess Kitchen [ Refraction index as a function of wave length ]
    • March 31 (W) - Wei-Yuen Tan [ Laser beam shaping in industrial applications ]
    • April 2 (F) - Tania Chan [ Holograms ]
    • April 5 (M) - Sonja Perreten [ Image transmission in flexible tubes ]
    • April 6 (T) - Yanny Cheng and Wesley Lam [ ] (in Mathematics 103, 1:00 - 2:00)
    • April 8 (Th) - Darren Ho [ Zoom lenses ] (in Mathematics 103, 1:00 - 2:00)
    • Sample examination questions based on the presentations