Glossary for Geometric Optics
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.
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.
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.
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
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 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.
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.
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.
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.
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.
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 =
is the dielectric constant for the medium.
is the law that determines how much a light ray bends when entering a medium of refractive index nt
from a medium of index ni
at an angle θi
to the normal.
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.
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.
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
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.
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.
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.
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.
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 90o to the normal to the
surface. This angle of incidence is called the critical angle, given by: sinθc = nt/ni. As the angle
of incidence increases beyond the critical angle, total internal reflection will occur.