I. Parabolic Reflector Lab Background page__

A. Light at Boundaries 1. The Law of Reflection The diagram below illustrates the law of reflection.

law of reflection The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

incident ray 2 (a) The ray of light approaching the mirror is known as the incident ray. reflected ray (b) The ray of light which leaves the mirror is known as the reflected ray (labeled R in the diagram). (c) A line can be drawn perpendicular to the surface of the mirror; this line is known as a normal line. (d) The angle between the incident ray and the normal is known as the angle of incidence. (e) The angle between the reflected ray and the normal is known as the angle of reflection.

B. Parabolic Reflector 1.A parabolic reflector has a concave mirror that reflects light from its inner (“caved in”) surface. 2.Parabolic reflectors used as solar cookers take the parallel beams of light that come from the sun and focus them at one point called the focal point.

3. A parallel beam is one which does not diverge or converge - its width stays the same as the light wave travels out from its source. The sun produces parallel beams. 4. A parabola has many uses within everyday life because it has the property of focusing to a point incident rays parallel to the axis. Automotive headlamps, microwave / radar antenna and most reflecting telescopes use parabolic surfaces in their designs to name a few.

C. Curved Mirror Terminology 1. Center of curvature (C) is the center of the sphere from which a spherical mirror is taken 1. Center of curvature (C) is the center of the sphere from which a spherical mirror is taken. Vertex (V) 2. Vertex (V) is the center of the mirror. Principal axis 3. Principal axis is the radius connecting the center of curvature of a curved mirror with its geometric vertex.

Base Reflector Principal Optical Axis Pot Focal Point 50°

4. Normal 4. Normal is the line drawn perpendicular to the mirror surface at the incidence point. Principal focus 5. Principal focus (F) is where the light rays converge to or diverge from. 6. Focal length ( f ) is the distance from the vertex to its principal focus. 7. The aperture determines the amount of light intercepted by the mirror.

principal focus 8. Incident light rays (or incoming light rays) are parallel to the principal axis and are reflected and converge at the principal focus. (This is where you will do your cooking.) Base Reflector Principal Optical Axis Pot Focal Point 50°

D. Parabolic Equation 1. The graphs of quadratic functions have the characteristic shape of a parabola, where y = ax 2 + bx + c, and the parabola can be mathematically defined as { y = x 2 / 4f }, where "x" is the radius of a dish and "f" is the focal length. 2. See diagram.

II. Construction A. After you have completed your graph, you will need to take the graph and cut out the shape of the parabola that you will use as your pattern for the construction of the spines. B. The pattern will then be laid down on the material you wish to make the solar cooker from, such as insulation board.

C. Lay the pattern down and cut out the spines.  Note: to keep the shape of the parabola and not have any sag in the shape, you may need at least 12 spines. (More would be better.) D. Once the spines are cut out, use a base board (made out of cardboard, wood, insulation board, etc.) to set the spines up in a circle.  It may help to draw a small circle no more than 1 inch (1 inch is 2.54 centimeters) in diameter in the center of the baseboard (use a small lid). Then set the spines up at the edge of this circle to keep everything uniform.

The circle doesn’t need to be more than around one inch in diameter Parabolic spines set up at edge of circle Baseboard

Note how the spines are set up

E. The spines can be hot glued, taped, or “sandwiched” in place by gluing blocks of material on either side of the spines to hold them in place. Spine Wedge

F. Once the spines are set up, you need to get some poster board (or possible cardboard) and cut it into pie slices).  These need to be a little larger than the size of the spacing of the spines on the baseboard. G. Find the reflective surface you are going to use and glue it onto the pie slices. Make sure you smooth as many wrinkles out of the material as you can. H. Next glue or tape these to the spines. I. Finally place a hotdog holder onto the project to hold the hotdog securely in place. *** Make sure this is longer than the focal point of the cooker so that the hot dog can be slid down in place.