A paraboloid is a 3D surface formed by rotating a parabola around its axis of symmetry. A hyperbolic paraboloid resembles a saddle. Parabolic mirrors and satellite dishes use the geometry of paraboloids to reflect and collect light and signals.
A paraboloid is a special type of three-dimensional surface. In the simplest case, it is the revolution of a parabola along its axis of symmetry. This type of surface will open upwards in both side dimensions. A hyperbolic paraboloid will open up in one dimension and down in the other, resembling a saddle. As in a two-dimensional parabola, scaling factors can be applied to the curvature of a paraboloid.
To understand how a paraboloid behaves, it is important to understand parabolas. In fact, some cross sections of a paraboloid will form a parabola. The equation y = x2 will form a parabola in a standard coordinate system. What this equation means is that the distances of a point on this line from the x and y axes will always have a special relationship to each other. The y value will always be the x value squared.
If you rotate this line around the y-axis, a simple circular paraboloid is formed. All vertical cross sections of this surface will open in the positive y direction. It is possible, however, to form a hyperbolic paraboloid which also opens downwards into the third dimension. Vertical cross sections in this case will have half of their parabolas opening in the positive direction; the other half will open in the negative direction. This surface of a hyperbolic paraboloid will look like a saddle and is called a saddle point in mathematics.
One application of the paraboloid surface is the primary mirror of a reflecting telescope. This type of telescope reflects incident light rays, which are nearly parallel if they come from far away, onto a smaller eyepiece. The primary mirror reflects a large amount of light to a smaller area. If you’re using a circular mirror, the reflected light rays don’t fit together perfectly at a focal point; this is called spherical aberration. Though more complicated to make, parabolic mirrors have the geometry needed to reflect all rays of light into a common focal point.
For the same reason as the parabolic mirror, satellite dishes commonly use a concave parabolic surface. Microwave signals sent by orbiting satellites are reflected off the surface towards the focal point of the dish. A mounted device called a feedhorn then collects these signals for use. Sending signals works in a similar way. Any signal sent from the focal point of a paraboloid surface will be reflected outward in parallel beams.
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