Geometric Optics
Geometric optics is the study of the path of light rays through systems of lenses, mirrors, and other media. English physicist and mathematician Sir Isaac Newton's Opticks published in 1704 formalized the description of image-formation in lenses and mirrors, providing the first thorough study of geometric optics.
The law of reflection states that the angle of an incident beam is equal to its angle of reflection. A medium that allows the passage of light without a change in velocity of light is said to have index of refraction (n) where the velocity of light propagation is determined as the velocity of light in a vacuum (c) divided by the index of refraction (n).
A ray of light that propagates across the interface (boundary) of two media (materials) obeys Snell's law of refraction. The media of incoming and outgoing rays, having indices of refraction n and n, respectively, refract (bend) light rays at their interface according to Snell's law (n sin = n sin ), where and are the incoming and outgoing angles that rays of light make with lines perpendicular (normal) to the interface.
The principle of (time) reversibility is the observation, generally true in optics and for all electromagnetic fields, that the laws for propagation of light rays are the same when the direction of time is reversed. For the laws of refraction and reflection, time reversal simply means that light rays travel in the opposite direction; the form of each law remains the same.
The laws of image formation state that the reconvergence of light rays determines the location of an image of the point source. After reconverging, the rays diverge again from the image point, producing an apparent ray source. The image of an extended object is a set of the images of the object's constituent point sources. The location, size, shape, and orientation of images produced by lenses and mirrors is given by the laws of image formation. The classical tools for image formation are mirrors and lenses.
An object at a very large distance forms an image at the focal plane of a lens or mirror. The focal length of a human eye is approximately 1 in (2.5 cm), where the focal plane is located on or in front of the retina. The focal length of the objective (far lens) of a 10 ft (30 m) long telescope is 10 feet. Compound lens and mirror systems allow the manipulation of images. A second lens can produce a secondary image of an image produced by a first lens.
A lens or mirror with focal length (f) placed a distance (s) from an object will form an image at distance s
where R and R are the radii of curvature of the lenses spherical surfaces.
Geometrical aberrations are the characteristics of a lens that prevent an ideal image from being formed. The total geometric aberration of a lens may be approximately decomposed into quantitative measurements of five primary geometric aberrations, described by Ludwig van Seidel in the 1850s. Astigmatism occurs when a lens's shape is such that the focal plane is different for perpendicular lines. Distortion causes the magnification of either the center or edges of an image, producing a pincushion or barrel-shaped bending of lines in the image. Curvature of field gives the deviation of the focal surface from a plane (where a true focal plane has zero curvature of field). Coma is the formation of a comet-shaped image for every point on the object. Spherical aberration, which is observed in spherical lenses, comes about when the focal lengths from different regions of a lens are different, preventing the formation of a well-defined focal plane.
In a wide variety of circumstances, the rules of geometric optics give a close approximation to the macroscopic behavior of light. They predict the characteristics of eye lenses and allow the design of telescopes, microscopes, cameras, eyeglasses, and countless other inventions. The principles of geometric optics have been extended to other fields, such as the design of magnetic lenses in particle accelerator beam lines that allow experimentalists to focus beams of high-energy particles. Analysis of multiple images of galaxies produced by light refraction by gravity (gravitational lensing) in space requires consideration of principles of geometric optics, as does the modeling of the propagation of acoustic disturbances in the earth. Geometric optics does not account for the wave nature of light, which causes interference and diffraction, nor does it explain light's quantum mechanical properties.
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