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In geometrical [[optics]], a '''focus''', also called an '''image point''', is the point where [[light]] rays originating from a point on the object converge [http://www.charfac.umn.edu/glossary/f.html]. Although the focus is conceptually a point, physically the focus has a spatial extent, called the ''blur circle''. This non-[[ideal]] focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's apertur]. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures.

In geometrical [[optics]], a '''focus''', also called an '''image point''', is the point where [[light]] rays originating from a point on the object converge [https://www.charfac.umn.edu/glossary/f.html]. Although the focus is conceptually a point, physically the focus has a spatial extent, called the ''blur circle''. This non-[[ideal]] focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's apertur]. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures.

An image, or image point or region, is '''''in focus''''' if light from object points is converged almost as much as possible in the image, and '''''out of focus''''' if light is not well converged.  The border between these is sometimes defined using a circle of confusion criterion.

An image, or image point or region, is '''''in focus''''' if light from object points is converged almost as much as possible in the image, and '''''out of focus''''' if light is not well converged.  The border between these is sometimes defined using a circle of confusion criterion.

A '''principal focus''' or '''focal point''' is a special focus:

A '''principal focus''' or '''focal point''' is a special focus:

*For a lens, or a [[sphere|spherical]] or [[parabola|parabolic]] [[mirror]], it is a point onto which collimated light parallel to the axis is focused. Since light can pass through a lens in either direction, a lens has two focal points - one on each side. The distance in air from the lens or mirror's principal plane to the focus is called the ''focal length''.

*For a lens, or a [[sphere|spherical]] or [[parabola|parabolic]] [[mirror]], it is a point onto which collimated light parallel to the axis is focused. Since light can pass through a lens in either direction, a lens has two focal points - one on each side. The distance in air from the lens or mirror's principal plane to the focus is called the ''focal length''.

For the ellipse, both the focus and the center of the directrix circle have finite coordinates and the radius of the directrix circle is greater than the distance between the center of this circle and the focus; thus, the focus is inside the directrix circle. The ellipse thus generated has its second focus at the center of the directrix circle.

For the ellipse, both the focus and the center of the directrix circle have finite coordinates and the radius of the directrix circle is greater than the distance between the center of this circle and the focus; thus, the focus is inside the directrix circle. The ellipse thus generated has its second focus at the center of the directrix circle.

For the parabola, the center of the directrix moves to the point at [[infinity]]. The directrix 'circle' becomes a curve with zero curvature, indistinguishable from a straight line. The two arms of the parabola become increasingly parallel as they extend, and 'at infinity' become parallel; using the principles of projective geometry, the two parallels intersect at the point at infinity and the parabola becomes a closed curve (elliptical projection).  

For the parabola, the center of the directrix moves to the point at [[infinite|infinity]]. The directrix 'circle' becomes a curve with zero curvature, indistinguishable from a straight line. The two arms of the parabola become increasingly parallel as they extend, and 'at infinity' become parallel; using the principles of projective geometry, the two parallels intersect at the point at infinity and the parabola becomes a closed curve (elliptical projection).  

To generate a hyperbola, the radius of the directrix circle is chosen to be less than the distance between the center of this circle and the focus; thus, the focus is outside the directrix circle. The arms of the hyperbola approach asymptotic lines and the 'right-hand' arm of one branch of a hyperbola meets the 'left-hand' arm of the other branch of a hyperbola at the point at infinity; this is based on the principle that, in projective geometry, a single line meets itself at a point at infinity. The two branches of a hyperbola are thus the two (twisted) halves of a curve closed over infinity.  

To generate a hyperbola, the radius of the directrix circle is chosen to be less than the distance between the center of this circle and the focus; thus, the focus is outside the directrix circle. The arms of the hyperbola approach asymptotic lines and the 'right-hand' arm of one branch of a hyperbola meets the 'left-hand' arm of the other branch of a hyperbola at the point at infinity; this is based on the principle that, in projective geometry, a single line meets itself at a point at infinity. The two branches of a hyperbola are thus the two (twisted) halves of a curve closed over infinity.  

==Astronomical significance==

==Astronomical significance==

In the [[gravity|gravitation]]al two-body problem, the orbits of the two bodies are described by two overlapping conic sections each with one of their foci being coincident at the center of mass (barycenter).

In the [[gravity|gravitation]]al two-body problem, the orbits of the two bodies are described by two overlapping conic sections each with one of their foci being coincident at the center of mass (barycenter).

 

== References ==

== References ==