Math and Optics

 

Three projects and several outreach events at Saint Bernard School (Uncasville, CT) have tried to answer the math student’s perennial question: “What do I have to learn this for?”  The goal of the first project (2013-2014) was to show students in pre-calculus applications of transcendental functions and matrices. The second project (2015-2016) introduced students in Calculus I to structured problem solving through Problem-Based Learning. The third project (2017-2018) focused on applications of math taught in middle school (grades 6, 7 and 8). 


Some of these activities are based on Dumpster Optics and require only inexpensive materials.
Others made use of specialized items. In all cases, the mathematics is brought to the fore -
what do I need to know that for?



Funding was provided in part by outreach grants from SPIE.



New activities will be added during the 2018-2019 academic year.



ACTIVITIES


1. Spreading Light – How does light spread as you go away from a small light bulb?

   

Math topics: square numbers, quadratic functions, graphing).
  

Requires only simple materials.

   PDF file with instructions, student handout and teacher notesSpreading_Light.pdf


2. Pinholes and Triangles – How can a pinhole make an image?


Math topics: similar triangles, ratio and proportion. Measurement with similar triangles has two alternate versions, indoors     predicting and measuring image size and outdoors measuring the height of a tree.

Requires only simple materials.  Optional: making an actual pinhole camera is a more complex process
but the materials are simple.


   Slides with instructions:  Pinholes_and_triangles_slides.pdf    

   Student handout - How a pinhole makes an image:  Part_1_Pinhole_Image_Observations.pdf

   Student handout - Measurements of image size:  Measurement-Predict_Pinhole_Image_Size.pdf

   Outdoor version of Measurements:  Measurement-How_tall_is_a_tree.pdf


  1. 3.Spectroscopy – What colors are given off by a glowing or reflecting source?


Math topics: Interpolation is used on a graphic to find the wavelength of the H alpha line in this quick exercise.


Can be done with simple materials (See Dumpster Optics Colors of Light lesson for creating a transmission grating from a CD. Gas spectrum images can be found on the web. Be sure to remove wavelength notations!)

   Slides with instruction: Spectroscopy_and_Interpolation_slides.pdf.   
   The spectrum can be projected as a class project, of printed for students to work on at their desks.