# Geometric Optics

### Glossary for Geometric Optics

Reflection  -  When a light ray is incident on an interface between two media, some portion of the light ray will usually remain in the incident medium, tracing a path such that the angle of the incident ray with respect to the normal is equal to the angle of the reflected ray with respect to the normal. Moreover, the incident and reflected rays, as well as the normal to the surface, all lie in the same plane.
Refraction  -  When a light ray is incident on an interface between two media, some portion of the light ray will usually be transmitted into the second medium. If the speed of light in the transmitting medium is different to the incident medium, this causes the light ray to change direction. This phenomenon is called refraction. The amount of refraction is determined by the ratio is the speed of lights in the two media, and the angle of the incident ray as given by Snell's Law.
Rays  -  A line drawn in space corresponding to the direction of flow of radiant energy of a lightwave. A light ray is always perpendicular to the wavefront of a light wave. Rays do not correspond to anything physical, but are mathematical constructs useful for visualizing the progress of waves.
Lens  -  A lens is any refracting device (corresponding to a discontinuity in a medium) that rearranges the distribution of transmitted energy. Lens do not have to be transparent to light, but can instead be used to redirect X-rays or microwaves. The most useful lenses have spherical surfaces and act to focus light rays to a point near the lens.
Concave  -  Concave surfaces are those that are thicker at the edges than in the middle (for a mirror with a planar reverse side). Concave lenses causes parallel rays to diverge from the central axis of the lens, and only produce virtual images. Concave mirrors cause parallel rays to converge towards the central axis of the mirror, and can produce real or virtual images.
Convex  -  Convex surfaces are those that are thinner at the edges than in the middle (for a mirror with a planar reverse side). Convex lenses causes parallel rays to converge towards the central axis of the lens, and produce real or virtual images. Convex mirrors cause parallel rays to diverge away from the central axis of the mirror, and only produce virtual images.
Dispersion  -  Is the phenomenon by which light the bending or refraction of light is dependent on its wavelength or frequency in a certain medium. This occurs because some frequencies are closer to the resonant frequencies of atoms in the medium, causing them to be propagated more effectively. This accounts for the dispersion of white light into a spectrum as it passes through a prism.
Dielectric  -  A medium in which the electrons can be displaced from an equilibrium position by the application of an electric field, but will return to its original configuration when the field is removed. Metals are not dielectrics, since the field will cause electrons to flow through the metal. The ease with which electrons can be displaced is measured by the dielectric constant ε .
Converging  -  A converging lens or mirror causes incident parallel rays to be transmitted or reflected at an angle such that they must eventually cross the central axis or the optical device. Converging lenses are convex, and converging mirrors are concave.
Diverging  -  A diverging lens or mirror causes incident parallel rays to be transmitted or reflected at an angle such that they never cross the central axis of the optical device (they may, however, appear to cross behind the device). Diverging lenses are concave, and diverging mirrors are convex.
Focus  -  The point to which parallel light rays reflected or refracted from a converging lens or mirror converge (cross at a point), usually on the central axis is called the focus or focal point. This also applies to the point from which light rays in a diverging mirror or lens appear to cross. The distance from the center of the mirror or lens to the focus is the focal length. The plane parallel to the plane of the mirror or lens containing the focus is the focal plane.
Index of refraction  -  The index of refraction is a measure of the density of a dielectric medium, and relates to the amount of bending experienced by a light ray as it enters that medium. The absolute index of refraction is given by n = c/v , where v is the speed of light in that medium. This is also equal to n = , where ε is the dielectric constant for the medium.
Snell's Law  -

 n isinθ i = n tsinθ t

is the law that determines how much a light ray bends when entering a medium of refractive index n t from a medium of index n i at an angle θ i to the normal.
Sign conventions  -  Are the rules that tell us how to apply the lens equation. Diverging lenses or mirrors have negative focal length, converging mirrors or lenses have positive focal lengths. For lenses, the distance to the object is positive if it is on the same side of the lens as that from which the light is coming (negative otherwise), and the distance to the image is positive if it is on the opposite side of the lens from that which the light is coming (negative otherwise). For mirrors, the image or object distance is positive if it is in front of the mirror and negative otherwise. The height of the object is positive if it is above the central axis and negative if it is below the central axis.
Virtual  -  Is an image or object with a negative image or object distance. It corresponds to images formed where light rays appear to cross, but in fact do not cross. It would not be possible to project a virtual image onto a screen. The image you see of yourself in a plane mirror is virtual.
Real  -  Is an image or object with a positive image or object distance. It corresponds to images formed where light rays actually cross. It is always possible to project a real image onto a screen placed at the position of the image.
Chromatic aberration  -  Aberration caused by the dispersive effects of refracting optical systems. Because light rays of different wavelengths (colors) bend by different amounts as they pass through dielectric media, each wavelength will converge to a slightly different focal point. This means that it is impossible to focus rays from a polychromatic source accurately. This prove problematic in large refracting telescopes.
Aberration  -  Any condition of an optical system which causes its behavior to deviate from the idealized realm of geometric or Gaussian optics is called an aberration. Monochromatic aberrations (those that arise when using light of a single frequency only) include spherical aberration, coma, astigmatism, field curvature and distortion. One of the most significant such aberrations is spherical aberration--this arises due to the results of geometric optics being approximations that only hold near the center of the lens.
Normal dispersion  -  Cases in which n , the index of refraction increases with frequency are called normal dispersion. This is normally the case because resonant frequencies of most materials are in the Ultra-Violet range, so increasing the frequency of visible light causes it to approach the resonant frequency.
Anomalous dispersion  -  When n , the index of refraction, decreases with increasing frequency, we have anomalous dispersion. The same material case be normally dispersive in some frequency ranges but anomalously dispersive in others.
Total internal reflection  -  When light is in a dense medium and is incident on an interface with a less dense medium, it is possible for all the light to be reflected and remain inside the denser medium (none is transmitted). This phenomenon is called total internal reflection.
Critical angle  -  When light is in a dense medium and is incident on an interface with a less dense medium, for a certain angle of incidence, the transmitted light will just graze the interface, being at 90 o to the normal to the surface. This angle of incidence is called the critical angle, given by: sinθ c = n t/n i . As the angle of incidence increases beyond the critical angle, total internal reflection will occur.

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