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Refraction can give the impression that Earth's surface is flat, curved more convexly than it is, or even that it is concave (this is what happened in various trials of the Bedford Level experiment). The phenomenon of variable atmospheric bending can be seen when distant objects appear to be broken into pieces or even turned upside down.
where R is the radius of the spherical surface, n 2 is the refractive index of the material of the surface, n 1 is the refractive index of medium (the medium other than the spherical surface material), is the on-axis (on the optical axis) object distance from the line perpendicular to the axis toward the refraction point on the surface (which ...
A spherical lens has an aplanatic point (i.e., no spherical aberration) only at a lateral distance from the optical axis that equals the radius of the spherical surface divided by the index of refraction of the lens material. Spherical aberration makes the focus of telescopes and other instruments less than ideal. This is an important effect ...
The Old Bedford River, photographed from the bridge at Welney, Norfolk (2008); the camera is looking downstream, south-west of the bridge. The Bedford Level experiment was a series of observations carried out along a 6-mile (10 km) length of the Old Bedford River on the Bedford Level of the Cambridgeshire Fens in the United Kingdom during the 19th and early 20th centuries to deny the curvature ...
If there is refraction at a collective spherical surface, or through a thin positive lens, O'2 will lie in front of O'1 so long as the angle u2 is greater than u1 (under correction); and conversely with a dispersive surface or lenses (over correction). The caustic, in the first case, resembles the sign > (greater than); in the second < (less than).
Each optical element (surface, interface, mirror, or beam travel) is described by a 2 × 2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system.
where is the index of refraction at the center of the lens and is the radius of the lens's spherical surface. [6] The index of refraction at the lens's surface is n 0 / 2 {\displaystyle n_{0}/2} . The lens images each point on the spherical surface to the opposite point on the surface.
Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n 1 and another medium with index of refraction n 2.