Dish or Parabola: Difference between revisions
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A Parabola is one of the “conic sections” and is defined as the locus (path) of a point that travels so that it is equidistant from a fixed point and a straight line. Algebraically this can be reduced to: | A Parabola is one of the “conic sections” and is defined as the locus (path) of a point that travels so that it is equidistant from a fixed point and a straight line. Algebraically this can be reduced to: | ||
< | <math> y = ax^2</math> where a is a constant | ||
More specifically, < | More specifically, <math> y = \frac{x^2}{4f} </math> where f is the focal length – distance from the curve to the focal point | ||
In the diagram above | In the diagram above: | ||
* the Y axis is central to the curve | * the Y axis is central to the curve | ||
* the tangent is a line that touches the curve at one point and has the same gradient as the curve at that point | * the tangent is a line that touches the curve at one point and has the same gradient as the curve at that point | ||
| Line 19: | Line 19: | ||
== Finding the focal length of a parabolic dish == | == Finding the focal length of a parabolic dish == | ||
< diagram to go here > | |||
<math> f = \frac {D^2}{16d} </math> where '''D''' is the diameter of the dish and '''d''' is the depth of the dish | |||
Revision as of 19:38, 4 August 2008
Parabolic Geometry
< diagram to be inserted here >
A Parabola is one of the “conic sections” and is defined as the locus (path) of a point that travels so that it is equidistant from a fixed point and a straight line. Algebraically this can be reduced to:
<math> y = ax^2</math> where a is a constant
More specifically, <math> y = \frac{x^2}{4f} </math> where f is the focal length – distance from the curve to the focal point
In the diagram above:
- the Y axis is central to the curve
- the tangent is a line that touches the curve at one point and has the same gradient as the curve at that point
- the normal is perpendicular to the tangent at the point of contact with the curve
- i is the angle of incidence – the angle between the incoming signal and the normal
- r is the angle of reflection – the angle between the reflected signal and the normal
- i = r Angle of incidence = Angle of reflection
- a broad beam entering the parabola will be reflected to and concentrated at the focal point
Finding the focal length of a parabolic dish
< diagram to go here >
<math> f = \frac {D^2}{16d} </math> where D is the diameter of the dish and d is the depth of the dish