Curved mirror in the context of "Catadioptric system"

A sphere (from Greek σφαῖρα, sphaîra) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and the distance r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.

The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings.

A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.

From the time of Newton to the 19th century, the mirror itself was made of metal – usually speculum metal. This type included Newton's first designs and the largest telescope of the 19th century, the Leviathan of Parsonstown with a 6 feet (1.8 m) wide metal mirror. In the 19th century a new method using a block of glass coated with very thin layer of silver began to become more popular by the turn of the century. Common telescopes which led to the Crossley and Harvard reflecting telescopes, which helped establish a better reputation for reflecting telescopes as the metal mirror designs were noted for their drawbacks. Chiefly the metal mirrors only reflected about 2⁄3 of the light and the metal would tarnish. After multiple polishings and tarnishings, the mirror could lose its precise figuring needed.

A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally, it was an optical instrument using lenses, curved mirrors, or a combination of both to observe distant objects – an optical telescope. Nowadays, the word "telescope" is defined as a wide range of instruments capable of detecting different regions of the electromagnetic spectrum, and in some cases other types of detectors.

The first known practical telescopes were refracting telescopes with glass lenses and were invented in the Netherlands at the beginning of the 17th century. They were used for both terrestrial applications and astronomy.

In optics, vergence is the angle formed by rays of light that are not perfectly parallel to one another. Rays that move closer to the optical axis as they propagate are said to be converging, while rays that move away from the axis are diverging. These imaginary rays are always perpendicular to the wavefront of the light, thus the vergence of the light is directly related to the radii of curvature of the wavefronts. A convex lens or concave mirror will cause parallel rays to focus, converging toward a point. Beyond that focal point, the rays diverge. Conversely, a concave lens or convex mirror will cause parallel rays to diverge.

Light does not actually consist of imaginary rays and light sources are not single-point sources, thus vergence is typically limited to simple ray modeling of optical systems. In a real system, the vergence is a product of the diameter of a light source, its distance from the optics, and the curvature of the optical surfaces. An increase in curvature causes an increase in vergence and a decrease in focal length, and the image or spot size (waist diameter) will be smaller. Likewise, a decrease in curvature decreases vergence, resulting in a longer focal length and an increase in image or spot diameter. This reciprocal relationship between vergence, focal length, and waist diameter are constant throughout an optical system, and is referred to as the optical invariant. A beam that is expanded to a larger diameter will have a lower degree of divergence, but if condensed to a smaller diameter the divergence will be greater.

In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. This phenomenon commonly affects lenses and curved mirrors, as these components are often shaped in a spherical manner for ease of manufacturing. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems. The effect of spherical aberration was first identified in the 11th century by Ibn al-Haytham who discussed it in his work Kitāb al-Manāẓir.