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For a diverging lens (for example a concave lens), the focal length is negative and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens. When a lens is used to form an image of some object, the distance from the object to the lens u, the distance from the lens to the image v, and the ...
For concave lenses, the focal point is on the back side of the lens, or the output side of the focal plane, and is negative in power. A lens with no optical power is called an optical window, having flat, parallel faces. The optical power directly relates to how large positive images will be magnified, and how small negative images will be ...
The focal length f is considered negative for concave lenses. Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens. Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens
R = radius of curvature, R > 0 for concave, valid in the paraxial approximation θ is the mirror angle of incidence in the horizontal plane. Thin lens f = focal length of lens where f > 0 for convex/positive (converging) lens.
The cardinal points were all included in a single diagram as early as 1864 (Donders), with the object in air and the image in a different medium. Cardinal point diagram for an optical system with different media on each side. F for Focal point, P for Principal point, NP for Nodal Point, and efl for effective focal length. The chief ray is shown ...
A lens contained between two circular arcs of radius R, and centers at O 1 and O 2. In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex).
In lens systems, aberrations can be minimized using combinations of convex and concave lenses, or by using aspheric lenses or aplanatic lenses. Lens systems with aberration correction are usually designed by numerical ray tracing. For simple designs, one can sometimes analytically calculate parameters that minimize spherical aberration.
The magnification of the virtual image formed by the plane mirror is 1. Top: The formation of a virtual image using a diverging lens. Bottom: The formation of a virtual image using a convex mirror. In both diagrams, f is the focal point, O is the object, and I is the virtual image, shown in grey. Solid blue lines indicate (real) light rays and ...