Glossary for Reflection, Refraction, and Optical Fibers

Angle of Entry
 (Generally identified as θ0.)  The angle of incidence made by light entering the end of an optical fiber.  (This is a term used by the author of these materials, not necessarily by others writing on the topic of optical fibers.) First used on this page of this module.

Angle of Incidence
 (Generally identified as θi, but sometimes as a "numbered" theta, such as θ1.)  The angle at which light strikes an interface between two media, measured between the path of the light and the normal to the interface.  The images to the right show the angle of incidence, θi, between the green incident ray and the dotted line representing the normal.  The image on the top depicts light being reflected at the interface, and the image on the bottom depicts light being transmitted and refracted at the interface.  See this page of this module to learn more about measuring the angle of incidence.

Angle of Reflection
 (Generally identified as θr, but sometimes as a "numbered" theta, such as θ2.)  The angle at which light is reflected by an interface between two media, measured between the path of the light and the normal to the interface.(In the figure to the right, the angle of reflection lies between the normal and the red reflected light beam and is denoted by θr). See this page of this module to learn more about reflection.

Angle of Refraction
 (Generally identified as a "numbered" theta, such as θ2, but sometimes as θr.) The angle at which light travels after passing through an interface between two media, measured between the path of the light and the normal to the interface.  See this page of this module to learn more about refraction.

Apex (Angle)
 The apex is the pointed tip of a cone.  The apex angle is the angle between the lines that define the apex, as shown to the left.

 The layer surrounding the core of an optical fiber, also transparent to light.  To trap light, the cladding must have a lower index of refraction than the core. The top image to the right shows a schematic of the core and cladding in a fiber.  The photo below shows an actual optical fiber next to a sewing needle; the cladding is the 125μm-wide glass layer covering the core.See this page of this module to learn more about why claddings are used.

Complementary Angles
 Two angles that add to give 90°, such as the two non-right angles in a right triangle, or the two angles on either side of a line that bisects a right angle.  In the image to the right, lines AP and BP create a right angle.  CP bisects this right angle.  Angles θ1 and θ2 are complementary, since they add to give 90°.  See this link to Math League for more information on complementary angles.

Cone of Acceptance
 A cone in space with its apex at the point light enters an optical fiber, opening away from the fiber, with an apex angle of twice the cut-off angle θ0max.  Light that travels into the fiber within this hypothetical cone (shaded in the image to the left) will be trapped by the fiber.  Light entering the fiber at an angle of entry outside the cone of acceptance will escape through the perimeter of the fiber.  This page of this module shows how to determine the cone of accepatance.

Core (of the Fiber)
 The central part of an optical fiber, through which the light primarily travels.  To trap light, the core must have a higher index of refraction than the next layer out (called the cladding).  In a step-index fiber, the core has a single index of refraction.  The top image to the right is a schematic of the core and cladding in a fiber.  The photo below shows an actual optical fiber next to a sewing needle;  the core is the material in the center measuring 62 μm wide.   See this page of this module to learn more about the makeup of optical fibers.

Critical Angle
 (Generally identified as θc.)  The minimum angle of incidence for which total internal reflection will occur at an interface between two particular media.  When light strikes an interface with an angle of incidence equal to the critical angle, the angle of refraction equals 90 degrees.  For any larger angle of incidence, the angle of refraction is not defined (since its sine becomes greater than 1.0, according to Snell's Law), and no light can pass over the interface. Applying Snell's Law gives the following expression for the critical angle of an interface between medium 1 and medium 2:  sin θc = n2 / n1.  For the critical angle to be defined, the medium (1) through which the light is initially traveling must have a greater index of refraction than the medium (2) on the other side of the interface. (In the image to the right, θ1equals the critical angle θc since the angle of refraction is 90 degrees).  The critical angle and total internal reflection are covered on this page (and the next one) of this module.

Cut-Off Angle
 (Generally identified as θ0max.)  The maximum angle of entry θ0 for which light will be trapped by an optical fiber.  Equals the half-angle at the apex of the cone of acceptance.  This page of this module introduces the cut-off angle.

Dense (Medium)
(A medium) having a relatively high index of refraction.  In some situations glass, with a typical index of refraction of 1.5, is considered a dense medium.  When compared to diamond's index of refraction of 2.4, however, glass  might be considered a rare medium.  (In these materials, dense and rare refer to optically dense and optically rare.  They do not refer to the mass density of a material.)

Diffuse Reflection
The reflection of a beam of light during which the light beam scatters in a wide range of directions, as described on this page of this module.  Also called specular reflection, it occurs when light is reflected by a rough surface such as a classroom wall.  Diffuse reflection is the opposite of total reflection, which is NOT the same as total internal reflection.

Dispersion
The spreading of light waves.  Chromatic dispersion refers to the separation of light into its constituent colors, as occurs with a prism. Check out this link to the Glenbrook Physics Classroom for more information on light dispersion.

Traveling electric and magnetic fields, with wave properties, which carry energy and momentum from one point to another.  Visible light is one category of electromagnetic radiation.  Radio waves, X-rays, microwaves, and gamma rays are other categories, which are distinguished by their wavelengths. See this link to the Glenbrook Physics Classroom for more information on electromagnetic radiation.

Electron
A fundamental particle with negative charge found in atoms.  It has a mass of 9.11 x 10-31 kilograms and a charge of -1.6 x 10-19 Coulombs.  Conduction occurs primarily from the movement of electrons through materials.  Click this link to go to the Particle Adventure webpage for more information on electrons.

Frequency
The number of cycles completed in each unit of time.    Only defined for a phenomenon that is periodic (repeats regularly) in time.  Equal to 1/period. Check out the Glenbrook Physics Classroom for more information about frequency.

An optical fiber with a continually varying index of refraction.  The index starts large along the center axis of the fiber and gradually decreases as light travels toward the perimeter of the fiber.  This graded index smoothly guides light toward the center axis of the fiber.  The fibers discussed in this module are of the simpler step-index construction.

Index of Refraction, n
The ratio of the speed of light in vacuum to the speed of light in the medium being considered.  Also determines how much the path followed by light bends, or refracts, when traveling from one medium to another.  Index of refraction is introduced on this page of this module.

Law of Reflection
Experimental observation that the angle of incidence equals the angle of reflection.  This is true not only of the reflection of light by a surface but is true in many mechanical situations as well. The law of reflection is discussed on this page of this module.

Medium (Media)
A particular type of substance, such as water, glass, or air.  "Media" is the plural of medium.

Normal
 Perpendicular, or a line perpendicular.  The normal to a surface is a line perpendicular to the surface at the point of intersection.  If the surface is not flat, the normal is perpendicular to a tangent line drawn through the point of intersection.  Interestingly, perpendicular is the original meaning of the word "normal".  The common usage meaning "ordinary" came about because ordinary things are often perpendicular. The normal lines to a bumpy surface are shown on this page of this module.

Numerical Aperture

A characteristic of optical fibers, indicating the size of the cone of light incident on a fiber's end which will remain within the fiber.  If the end of the fiber is surrounded by air, the numerical aperture is just the sine of the cut-off angle θ0maxfor the fiber.  If a medium of index n0 surrounds the end of the fiber, the numerical aperture is defined by

NA = n0 sin θ0max,
The numerical aperture is a function of the fiber, independent of how it is used.  Geometry can be used (and was on this page) to show
NA = (n12- n22)1/2,
where n1 is the index of refraction of the core of the fiber, and n2 is the index of refraction of the cladding of the fiber.

Optical Fiber (Fiber Optic Cable)
 A tube, generally of glass or plastic, that guides light through its length by using refraction.  Optical fibers have the capability of transferring large amounts of information with little loss when the information is contained in characteristics of a beam of light.  The photo to the right shows a magnified view of a step-index optical fiber, placed next to a sewing needle.  The core and cladding of the fiber have been uncovered, and their diameters indicated, in the photo.

Period
The time passing before a cycle repeats.  Only defined for a phenomenon that is periodic (repeats regularly) in time.  Equal to 1/frequency. Check out the Glenbrook Physics Classroom for more information on periods.

Rare (Medium)
(A medium) having a relatively low index of refraction, such as air, which has an index of refraction of 1.003.  (In these materials, rare and dense refer to optically rare and optically dense.  They do not refer to the mass density of a material.)

Refraction
Bending, as occurs when light travels from one medium to another.  The discussion of refraction begins on this page of this module.

Snell's Law
The relationship describing how light bends at the interface of two media.  Descartes also studied this phenomenon (but later than Snell did), and it is his mathematical formulation of the effect that we call Snell's Law:
n1 sin θ1 = n2 sin  θ2,
where ni is the index of refraction in the ith medium, and  θi is the angle in the ith medium, measured between the path of light and the normal to the interface.  Snell's Law is introduced on this page of this module.

Speed of Light in Vacuum, c
The ultimate speed limit of the universe.  Information cannot travel any faster than c, which equals 3.00 x 108 meters per second.

Standing wave
A wave with fixed "nodes" which always have zero displacement, and "anti-nodes" that oscillate between the maximum value (amplitude) of the wave and the minimum value (negative the amplitude).  Formed when two identical traveling waves moving in opposite directions combine.  Sinusoidal standing waves have the form
y(x,t) = ym sin (kx) cos ωt.
Check out the Glenbrook Physics Classroom for more information on standing waves.

Step-Index Fiber
 An optical fiber consisting of a core with a single uniform index of refraction,  surrounded by a cladding with another single uniform index of refraction.  The index of refraction "steps down" as light travels from the core to the cladding.  When graphed as a function of distance from the fiber axis, the index of refraction has the shape of a step function.  Light is trapped in a step-index fiber by total internal reflection.

Step Function
 A two-leveled function, equaling one level for one range (region 1) of the independent variable and the other level for the remaining values (region 2) of the independent variable.  Check out this link to MathWorld for more information on step functions.

Tangent
 A line in the "direction" of the surface at the intersection point.  Mathematically, the tangent is a straight line with a slope equal to the slope of the surface at the point of intersection.  In the image to the right, the blue line is the tangent to the black surface at the red point of intersection. Check out this link to MathWorld for more information.

Total Internal Reflection (TIR)
 The phenomenon in which light is trapped (totally internally reflected) in one medium, because the refracted ray cannot exist (mathematically, according to Snell's Law, the sine function becomes greater than 1.0). Occurs when light traveling from a denser medium to a rarer medium strikes the interface at an angle of incidence greater than the critical angle for that interface.  When this condition is met, light cannot be transmitted through the interface and so is all reflected back into the original material.  The image to the left shows TIR just starting to occur, as the angle of incidence equals the critical angle. The critical angle and total internal reflection are covered on this page (and the next one) of this module.  Not to be confused with total reflection.

Total Reflection
The reflection of a beam of light during which the light beam remains collimated and does not scatter, as described on this page of this module.  Occurs when light is reflected by a smooth surface such as a flat mirror.  The opposite of diffuse reflection and not to be confused with total internal reflection.

Traveling Wave
A wave that propogates in both space and time.  Sinusoidal traveling waves have the form
y(x,t) = ym sin (kx - ωt)
Check out the Glenbrook Physics Classroom for more information on traveling waves.

Vacuum
The absence of matter.  Outer space is very close to a pure vacuum, with an average of .07 particles found in every cubic meter.

Vertical Angles
 Angles that are equal and opposite from each formed by the intersection of two lines. In the image to the right, angles ABC and DBE (highlighted in blue) comprise a pair of vertical angles; ABD and CBE (highlighted in purple) comprise a second pair.  Check out this link to MathLeague for more information on vertical angles.

Wave
A mechanism by which some quantity, such as energy or information, is moved from point A to point B without an individual particle traveling the entire distance between point A and B.  Consider a sports stadium.  The message "I'm excited" is sent around the stadium by fans doing "the wave" without those individual fans moving from their seats.  Check out the Glenbrook Physics Classroom for more information on waves.

Wavelength
Often denoted by the Greek letter λ.  The distance between starting points (or between ending points or between any other identical points) of adjacent cycles.  Only defined for a phenomenon that is periodic (repeats regularly) over distance.  Equal to wave speed times the period of a traveling wave.  The wavelength of light determines its color. Go to the Glenbrook Physics Classroom for more information on wavelengths.