Concavity

• The word "concave" is defined the Free Merriam-Webster Dictionary as "hollowed or rounded inward like the inside of a bowl." Regardless of its specific shape, the reflection of light from a concave surface produces magnified images of close-by objects and a convergence of light from distant ones.
  
  

Shapes

• The concave surface may follow any number of shapes. Cylindrical surfaces have a circular cross section in a single plane, and spherical ones are circular in all directions. The most useful concave shape is one that has a parabola as its cross-section in all planes.
  
  

Spheres and Aberration

• A sphere is a three-dimensional object with the cross section of a circle. A spherical mirror is a section of a sphere. It concentrates light that strikes near its central axis toward a focal point that is a distance of one half the circular radius from the surface.
  
  In optics, aberration is the term applied to the degradation of image quality. If a spherical reflector covers a wide enough arc, the outside edges produce a focus that deviates significantly from the focus of light that reflects directly along its axis. This is known as spherical aberration.
  
  

Parabolas

• A parabola is a conic section, like a circle. It is a collection of points that are equidistant from a point that serves as its focal point and a line called the directrix. The Parabola has a line of symmetry running through its focal point and forming a right angle with the directrix, which is located behind the figure.
  
  The formula for a parabola is x (squared) = 4ay, or y (squared) = 4ax, depending on whether the figure is horizontal or vertical. The parameter a is the minimum distance of the curve from its focus and directrix line, which occurs at the tip of the parabola.
  
  

Parabolic Mirrors

• Parabolic reflectors have the unique property of focusing all parallel rays of light that enter parallel to the line of symmetry from a distant object at only the single focal point. Thus, there is no aberration from the shape no matter how large the diameter is in relation to the focal point of the parabola.