What I came up with was...the parabola. So by using the properties of parabolas, we're going to cook a hot dog. Essentially, we're using math to cook hot dogs :D
I believe I've just proven that I'm a nerd? Oh well, I'm in good company here.
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Signing UpStep 1How it works
The way it applies to us, is that the light that hits the parabola, will reflect back to one intersection point. That intersection point is called the point of focus. By placing the hot dog in the point of focus, all of the sun's rays that hit anywhere in the cooker, will reflect onto the hot dog...thus cooking it.
Click here to see how the light reflects
By the way...the shape of the entire cooker is a parabolic trough.
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I made this, and cooked a wiener, i also took a old meat thermometer and put it at the focus point of the oven, which i accidentally made sideways, so its like a big, curvy rectangle, and i got to 175 degrees Fahrenheit, when i cooked the wiener, it only got to 135 about unfortunately
Parabola's are usually deeper than plain concave reflectors, like satelite dishes are just concave parabola's, with longer focal lengths. There is a difference. I call satelite dishes, old search lights, concave shapes, and parabola's have two different shapes, deeper than concave dish reflectors with very long focal lengths, where the parablola has a short focal length.
I'm not disputing it is concave or not, I hope you can see the point I am trying to convey in my question. My satelite dish search light and older search lights that used dish reflectors, were concaves with very long focal lengths compared to true parabola's that have very short focal lengths like flashlights, headlights, modern search lights... I'm writing you right now using a parabola dish with a short focal length concentrating my wifi signal to my antenna just an inch from the center of the reflector, I made from a link on here at Instructables. Thus keeping my focal point very short. See what I am trying to say? Pretty soon I will add a satelite dish reflecting my signal to the parabola to gain even more signal strength to continue running the wifi at full potential at 48 Mbps speeds. Right now I am only getting enough signal to hit 18 Mbps speeds. I don't dispute parabola's are concave, simply asking what kind of parabola are you using in your search light?
Also, in Step 1, you link to this image. I attached a modified version that better illustrates the reflection. If you want to use it, feel free.
Here's my caption on that image: "Parabolic curve showing arbitrary line (L), focus (F), and vertex (V). L is an arbitrary line perpendicular to the axis of symmetry and opposite the focus of the parabola from the vertex (i.e. farther from V than from F.) The length of any line F - Pn - Qn is the same. This is similar to saying that a parabola is an ellipse, but with one focal point at infinity."