Because a catenaric or hyperbolic arch - or any other type of mirror - won’t disperse the light rays from the incandescent light bulb at the focus in as efficient a manner, Sweetie.
The main thing unique about a parabola is that when a source of light (or electromagnetic rays) enters its cone in a line perpendicular to its closed conal tip, the rays that bounce off the walls of the cone will converge at one point: Its focus. For this reason, parabolic dishes are used to gather information from satellites. This is why your TV satellite dish (if it’s 17 or 18 inches in diameter) has a device 13 or 14 inches in front of the center of the dish. The concave surface of that dish is a very small part of the tip of a parabolic cone. The dish is positioned to look directly at a satellite in space that’s in fixed orbit, meaning the satellite is always in the same position in relation to the ground your living on. There are several such satellites around the world, so that any point on earth will always have access to a satellite. All signals broadcast to the dish in your yard will reflect off the concave surface of your dish, and be directed to the device at its focus. This device decodes the signals, amplifies them, and then sends them to your television, or - if it doesn’t decode the signals - sends them to a box by your TV that does that job.
The mirror in a flashlight works on the same principle, but backwards. The light bulb therein is set at the focus of the parabolic cone. The bulb sends out light in all directions, but the light rays that hit the inner surface of the parabolic mirror are reflected away in lines that are parallel to the shaft of the flashlight, if it so be that the shaft is the conventional battery-bearing tube in most flashlights. The reason why all flashlights thusly built show a dark spot in the middle of its beam, is because less light is reflected in that spot due to the presence of the device holding the light bulb. Light going directly toward the tip of the cone would bounce straight back out, where the bulb is, if the bulb’s bracket weren’t there.
If you’re an inventor, you could be famous and/or rich, some day, if you invented a flashlight that did not inhibit the reflected light at the tip of its parabolic cone.
Parabolic cones are also used in solar stoves or heaters, though often - if it’s a heater - a cone is replaced by a cylinder-type open tube that is bent along a parabolic curve. Thus, the focus of a parabolic cylinder is a continual line running along the length of the cylinder a specified distance from the unilateral bend of the parabolic arch. A tube - sometimes coiled up - is placed along this focus so to be in continual contact with the reflected, concentrated rays of the sun. Such devices that depend on the sun are often fitted with a light-sensitive switch that is placed below a sun shield. When the sun moves, causing the shadow of the shield to move off the switch, the switch is activated and a series of motors and gears are put into action to position the device so that it directly faces the sun again. Sometimes, if the heating device is too big and/or bulky, it doesn’t move at all, but a system that is built to follow the sun refracts or reflects the sun’s rays into the device.
You can build your own solar stove or food-warmer. I cannot guarantee any results, because I have not yet built one. But I can take you through the basic steps, and leave the trial and error to you. Perhaps sometime in the near future, I will make one and write a hub that gives specifics. Or, maybe you’ll beat me to the punch. For now, I’ll refer you to some hubs that teach related topics, at the foot of this article.
First, you must plot the parabolic arch. You can do this by using this formula: Y=X2/4P where Y is a number for height, X is a number for distance from point zero, and P is the place you want to put your focal point, or the parabola’s “focus.”
Just make a graph like the one in Fig. 3 (you don’t need the tenths (the red lines) if you don’t want to take the time; you can probably just visualize where the points go).
Next, decide how far from the bottom of the dish you want your focal point or “focus.” If your dish will be eight to ten feet wide, I recommend the point be two feet from the bottom. Whatever that number is, it will take the place of P in the formula. Here, I’m making it 2.
Use a box like the one in Fig. 4 to do your calculations. Or, you can just use my calculations as shown. Start by giving X the value of zero. This will result in Y being zero as well. Hence the first set of numbers is 0,0. I went in increments of halves, so that I could get a less choppy curve. If you wanted an even smoother grade, you could go quarters, or eighths. My next value for X is 0.5, since I’m incrementing in halves. This, after solving the above formula with X as being 0.5, results in Y being .031. So the second set of numbers is 0.5,0.031. The third set of numbers is 1,0.125, and so on until we get to 4,2. I stopped at the number 4, which would give me an eight-foot dish, if each number represents one foot. To get a smaller dish, just stop at a smaller number.
Each set of the numbers arrived at above has, as you’ve seen, two parts: The first number represents a value or place along the horizontal or X axis, and the second one represents a place on the vertical, or Y axis. These number sets will help us put dots on the graph. The First dot will be at point zero on both axes, because the set reads 0,0. The second dot will be halfway between zero and one, and at the height of .031, which is about a third of a tenth of an inch. The third dot will be placed on the one-inch line, and at the height of 0.125, which is 1/8th of an inch.
Once you’re done with the graph, you’ll have one-half of the parabolic arch. Put your graph over a piece of plywood and cut the wood with a jigsaw. With that piece, you now have a template to make as many more arches as needed to make a parabolic cone. Fan these arches in a circle, fasten them together, then put something at the focus point (two inches above the bottom in the case of my sample) that will house whatever you want to cook or warm.
Line the inner cone with cardstock, and on that put tin foil.
Another way to make a parabolic arch is to cut off a section of cone (See Fig. 5). The cut line should run parallel to any given straight line on the cone between its point, and a point on its mouth. It may be difficult making this line, or the cut, unless the cone is solid and you can prop it so that the cut line is parallel to the line between the point and the mouth.
Either way, you now have an un-tested parabolic dish for heat or for food-warming, or for whatever you want to use it for, and you are also armed with another answer to those endless “Mommy -- why” questions.
Samuel E. Richardson (author) from Salt Lake City, Utah on September 13, 2016:
SamboRambo on September 13, 2016:
Thank You, Naeem,
I'm a magnet for science gadgets, and I read a lot.
Samuel E. Richardson (author) from Salt Lake City, Utah on May 15, 2012:
Topaz, I would try to invent something, but my last query for another invention made me realize I need mucho dinero, which I don't have, on account of being retired.
If you try it, let me know how it goes.
topaz blue on May 11, 2012:
'If you’re an inventor, you could be famous and/or rich, some day, if you invented a flashlight that did not inhibit the reflected light at the tip of its parabolic cone'- why don't you ?
Very interesting and informative hub.
Mr. Bean on May 02, 2012:
I loved this! I'm a high school math teacher teaching parabolic equations and was searching for some nice applications to present to students (beyond the typical satellite dish) and came across this. Nice explanations and good examples. Thanks SamboRambo!
Samuel E. Richardson (author) from Salt Lake City, Utah on June 24, 2011:
Thank you all, for your comments and your visit. Silver, I've always been drawn to scientific tidbits. Also, during each day, I keep part of my mind focussed on each event or stimulus around me for the purpose of getting new ideas. I also draw from the jobs I've had, and my experience. Being old, this give me an advantage, since the older you get, the more (colorful?) stories you can tell.
Silver Poet from the computer of a midwestern American writer on June 22, 2011:
Fascinating. How do you come up with such unique ideas? I love flashlights. I tend to own more than I need of them, because I am always buying one for "backup" in case the ones I have fail in a crisis. Good educational hub.
Mandrake_1975 from Pennsylvania on June 22, 2011:
Great hub and very educational! Voted up.
Brinafr3sh from West Coast, United States on June 21, 2011:
This is an interesting hub on parabolic concave mirrors. (kinda went over my head).