Reflective Properties of Conic Sections

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number of rays
7
locator x-offset
0
ray length
10
locator y-offset
0
reflective curve
2
x
25
+
2
y
16
1
reset source
Conic sections, that is, ellipses, hyperbolas, and parabolas, all have special reflective properties. If the source of a signal is placed at one of the two focal points of an ellipse, the signal will be reflected to the other focal point. If the source is placed at one of the two focal points of a hyperbola, the signal will be reflected directly away from the other focal point. If the source is located at the one focus of a parabola, the signal will be reflected in lines parallel to the parabola's axis.

Details

Choose one of five reflective curves. All but the last are conic sections; the last one will show no coherent reflective property, no matter where the source is placed.
Rays emanate from the source. Choose the desired number of equally spaced rays using the "number of rays" slider. Choose how long the signal is from the source using the "ray length" slider.
Choose the source of the signal by dragging the locator, or using the "locator
x
-offset" and "locator
y
-offset" sliders.
The source starts at one of the focal points for all the conic sections. If you move the source and want it returned to the original focus, click the "reset source" checkbox.

External Links

Conic Section (Wolfram MathWorld)
Ellipse (Wolfram MathWorld)
Focus (Wolfram MathWorld)
Hyperbola (Wolfram MathWorld)
Parabola (Wolfram MathWorld)

Permanent Citation

Robert Baker, Steven Wilkinson
​
​"Reflective Properties of Conic Sections"​
​http://demonstrations.wolfram.com/ReflectivePropertiesOfConicSections/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011