Vergence (optics) in the context of "Lens"

In geometrical optics, a focus, also called an image point, is a point where light rays originating from a point on an object converge. 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. Even in the absence of aberrations, the smallest possible blur circle is the Airy disc caused by diffraction from the optical system's aperture; diffraction is the ultimate limit to the light focusing ability of any optical system. Aberrations tend to worsen 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.

A mirror, also known as a looking glass, is an object that reflects an image. Light that bounces off a mirror forms an image of whatever is in front of it, which is then focused through the lens of the eye or a camera. Mirrors reverse the direction of light at an angle equal to its incidence. This allows the viewer to see themselves or objects behind them, or even objects that are at an angle from them but out of their field of view, such as around a corner. Natural mirrors have existed since prehistoric times, such as the surface of water, but people have been manufacturing mirrors out of a variety of materials for thousands of years, like stone, metals, and glass. In modern mirrors, metals like silver or aluminium are often used due to their high reflectivity, applied as a thin coating on glass because of its naturally smooth and very hard surface.

A mirror is a wave reflector. Light consists of waves, and when light waves reflect from the flat surface of a mirror, those waves retain the same degree of curvature and vergence, in an equal yet opposite direction, as the original waves. This allows the waves to form an image when they are focused through a lens, just as if the waves had originated from the direction of the mirror. The light can also be pictured as rays (imaginary lines radiating from the light source, that are always perpendicular to the waves). These rays are reflected at an equal yet opposite angle from which they strike the mirror (incident light). This property, called specular reflection, distinguishes a mirror from objects that diffuse light, breaking up the wave and scattering it in many directions (such as flat-white paint). Thus, a mirror can be any surface in which the texture or roughness of the surface is smaller (smoother) than the wavelength of the waves.

A dioptre (British spelling) or diopter (American spelling), symbol dpt or D, is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dpt = 1 m. It is normally used to express the optical power of a lens or curved mirror, which is a physical quantity equal to the reciprocal of the focal length, expressed in metres. For example, a 3-dioptre lens brings parallel rays of light to focus at 1⁄3 metre. A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge. Dioptres are also sometimes used for other reciprocals of distance, particularly radii of curvature and the vergence of optical beams.

The main benefit of using optical power rather than focal length is that the thin lens formula has the object distance, image distance, and focal length all as reciprocals. Additionally, when relatively thin lenses are placed close together their powers approximately add. Thus, a thin 2.0-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a single 2.5-dioptre lens.

In optics, the image of an object is defined as the collection of focus points of light rays coming from the object. A real image is the collection of focus points made by converging rays, while a virtual image is the collection of focus points made by backward extensions of diverging rays. In other words, a virtual image is found by tracing real rays that emerge from an optical device (lens, mirror, or some combination) backward to perceived or apparent origins of ray divergences.

There is a concept virtual object that is similarly defined; an object is virtual when forward extensions of rays converge toward it. This is observed in ray tracing for a multi-lenses system or a diverging lens. For the diverging lens, forward extension of converging rays toward the lens will meet the converging point, so the point is a virtual object.