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This glossary is not intended to be complete. It focuses on those terms which give students particular difficulties. Some words have subtle and intricate meanings which cannot be encapsulated in a short definition. That's why textbooks exist. A good glossary for elementary physics may be found in Appendix G-1 of Kirkpatrick & Wheeler, Physics, A World View, Saunders, 1992.

This document is continually under development and may never be
finished.

**Absolute uncertainty.** The uncertainty in a measured quantity is due
to inherent variations in the measurement process itself. The uncertainty
in a result is due to the combined and accumulated effects of these
measurement uncertainties which were used in the calculation of that
result. When these uncertainties are expressed in the same units as the
quantity itself they are called *absolute uncertainties*.
Uncertainty values are
usually attached to the quoted value of an experimental measurement or
result, one common format being: (quantity) ± (absolute uncertainty
in that quantity).

Compare: relative uncertainty.

**Action.** This technical term is a historic relic of the 17th
century, before energy and momentum were understood. In modern
terminology, action has the dimensions of energy×time. Planck's
constant has those dimensions, and is therefore sometimes called
*Planck's quantum of action*. Pairs of measurable quantities
whose product has dimensions of energy×time are called
*conjugate quantities* in quantum mechanics, and have a
special relation to each other, expressed in Heisenberg's
uncertainty principle. Unfortunately the word *action* persists in
textbooks in meaningless statements of Newton's third law: 'Action
equals reaction.' This statement is useless to the modern student,
who hasn't the foggiest idea what action is.
See: Newton's 3rd law
for a useful definition.
Also see Heisenberg's uncertainty principle.

**Avogadro's constant.** Avogadro's constant has the unit
*mole ^{-1}.* It is

One *must* specify whether the value of Avogadro's constant is
expressed for a
gram-mole or a kilogram-mole. A few books prefer a kilogram-mole.
The unit name for a gram-mole is simply *mol*.
The unit name for a kilogram-mole is *kmol*.
When the kilogram-mole is used, Avogadro's constant should
be written: 6.02252 x 10^{26} kmol^{-1}. The fact that
Avogadro's constant
has units further convinces us that it is **not** 'merely a number.'

Though it seems inconsistent, the SI base unit is the gram-mole. As Mario Iona reminds me, SI isIs Avogadro's constant just a number? What about those textbooks which say 'You could have a mole of stars, grains of sand, or people.' In science wenotan MKS system. Some textbooks still prefer to use use the kilogram-mole, or worse, use itandthe gram-mole. This affects their quoted values for the universal gas constant and the Faraday Constant.

The reciprocal of Avogadro's constant is numerically equal to the unified atomic mass unit, u, that is, 1/12 the mass of the carbon 12 atom.

1 u = 1.66043 x 10^{-27} kg = 1/6.02252 x 10^{23}
mole^{-1}.

**Because.** Here's a word best avoided in physics. Whenever it appears
one can be almost certain that it's a *filler* word in a sentence
which says nothing worth saying, or a word used when one can't think of a
good or specific reason. While the use of the word *because* as a
link in a chain of logical steps is benign, one should still replace it
with words more specifically indicative of the type of link which is
meant. See: why.

Illustrative fable:The seeker after truth sought wisdom from a Guru who lived as a hermit on top of a Himalayan mountain. After a long and arduous climb to the mountain-top the seeker was granted an audience. Sitting at the feet of the great Guru, the seeker humbly said: 'Please, answer for me the eternal question: Why?' The Guru raised his eyes to the sky, meditated for a bit, then looked the seeker straight in the eye and answered, with an air of sagacious profundity,'Because!'

Capacitors for use in circuits consist of two conductors (plates). We
speak of a capacitor as 'charged' when it has charge Q on one plate, and
-Q on the other. Of course the net charge of the entire object is zero;
that is, the charged capacitor hasn't had net charge added to it, but has
undergone an internal separation of charge. Unfortunately this process is
usually called *charging* the capacitor, which is misleading
because it suggests adding charge to the capacitor. In fact, this process
usually consists of moving charge from one plate to the other.
The capacity of a single object, say an isolated sphere, is determined by
considering the *other plate* to be an infinite sphere surrounding
it. The object is given charge, by moving charge from the infinite sphere,
which acts as an infinite charge reservoir ('ground'). The potential
*of the object* is the potential between the object and the
infinite sphere.

Capacitance depends only on the geometry of the capacitor's physical
structure and the dielectric constant of the material medium in which the
capacitor's electric field exists. The size of the capacitor's capacitance
is the same whatever the charge and potential (assuming the dielectric
constant doesn't change). This is true even if the charge on both plates
is reduced to zero, and therefore the capacitor's potential is zero. If a
capacitor with charge on its plates has a capacitance of, say, 2
microfarad, then its capacitance is also 2 microfarad when the plates
have no charge. This should remind us that C = |Q/V| is
**not** by itself the *definition* of capacitance, but merely a
formula which allows us to relate the capacitance to the charge and
potential *when* the capacitor plates have equal and opposite
charge on them.

A common misunderstanding about electrical capacitance is to assume that capacitance represents the maximum amount of charge a capacitor can store. That is misleading because capacitors don't store charge (their total charge being zero) but their plates have equal and opposite charge. It is wrong because the maximum charge one may put on a capacitor plate is determined by the potential at which dielectric breakdown occurs. Compare: capacity.

We probably should avoid the phrase 'charged capacitor' or 'charging a capacitor'. Some have suggested the alternative expression 'energizing a capacitor' because the process is one of giving the capacitor electrical potential energy by rearranging charges in it.

**Capacity.** This word is used in names of quantities which express
the *relative* amount of some quantity with respect to a another
quantity upon which it depends. For example, heat capacity is dU/dT, where
U is the internal energy and T is the temperature. Electrical capacity, or
*capacitance* is another example: C = |dQ/dV|, where Q is
the magnitude of charge on each capacitor plate and V is the potential
diference between the plates.

**Centrifugal force.** When a non-inertial rotating coordinate system
is used to analyze motion, Newton's law **F** = m**a** is **not**
correct unless one adds to the real forces a *fictitious force*
called the *centrifugal force*. The centrifugal force required in
the non-inertial system is equal and opposite to the *centripetal
force* calculated in the inertial system. Since the centrifugal and
centripetal forces are concepts used in *two different*
formulations of the problem, they can not in any sense be considered a
pair of reaction forces. Also, they act on the same body, not different
bodies.
See: centripetal force,
action,
and inertial systems.

**Centripetal force.** The *centripetal force* is the radial
component of the net force acting on a body when the problem is analyzed
in an inertial system. The force is inward toward the instantaneous center
of curvature of the path of the body. The size of the force is
mv^{2}/r, where r is the instantaneous radius of curvature.
See: centrifugal force.

**cgs.** The system of units based upon the fundamental metric
units: centimeter, gram and second.

**Classical physics.** The physics developed before about 1900,
before we knew about relativity and quantum mechanics.
See: modern physics.

**Closed system**. A physical system on which no outside
influences act; closed so that nothing gets in or out of the
system and nothing from outside can influence the system's observable
behavior or properties.

Obviously we could never make measurements on a closed system unless we
were in it^{†}, for no information about it could get out of it!
In practice we loosen up the condition a bit, and only insist that there
be no interactions with the outside world which would affect those
properties of the system which are being studied.

† Besides, when the experimenter is a part of the system, all sorts of other problems arise. This is a dilemma physicists must deal with: the fact that if we take measurements, we are a part of the system, and must be very certain that we carry out experiments so that fact doesn't distort or prejudice the results.

Example: In a closed system, the charge, mass, total energy, linear momentum and angular momentum of the system are conserved. (Relativity theory allows that mass can be converted to energy and vice-versa, so we modify this to say that the mass-energy is conserved.)

**Misuse alert.**
A very common mistake found in textbooks is to speak of 'flow of
current'. Current itself is a flow of charge; what, then, could 'flow
of current' mean? It is either redundant, misleading, or wrong.
This expression should be purged from our vocabulary.
Compare a similar mistake: 'The velocity moves West.'

**Data.** The word *data* is the plural of *datum*.
Examples of correct usage:

'The data are reasonable, considering the…'

'The data were taken over a period of three days.'

'How well do the data confirm the theory?'

**Dimensions.** The fundamental measurables of a unit system in
physics—those which are defined through operational definitions. All
other measurable quantities in physics are defined through mathematical
relations to the fundamental quantities. Therefore any physical measurable
may be expressed as a mathematical combination of the dimensions.
See: operational definitions.

Example: In the MKSA (meter-kilogram-second-ampere) system of units, length, mass, time and current are the fundamental measurables, symbolically represented by L, M, T, and I. Therefore we say that velocity has the dimensions LT^{-1}. Energy has the dimensions ML^{2}T^{-2}.

**Empirical law.** A law strictly based on experiment, which may
lack theoretical foundation.

**Electricity.** This word names a branch or subdivision of
physics, just as other subdivisions are named ‘mechanics’,
‘thermodynamics’, ‘optics’, etc.

Misuse alert:Sometimes the wordelectricityis colloquially misused as if it named a physical quantity, such as 'The capacitor stores electricity,' or 'Electricity in a resistor produces heat.' Such usage should beavoided!In all such cases there's available a more specific or precise word, such as 'The capacitor storeselectrical energy,' 'The resistor is heated by the electriccurrent,' and 'The utility company charges me for theelectric energyI use.' (I am not being charged based on thepower, so these companies shouldn't call themselvesPowercompanies. Some already have changed their names to something like '... Energy')

The statement 'Energy is a property of a body' needs clarification. As with many things in physics, the size of the energy depends on the coordinate system. A body moving with speed V in one coordinate system has kinetic energyMisuse example:'The earth's auroras—the northern and southern lights—illustrate how energy from the sun travels to our planet.' —Science News, 149, June 1, 1996. This sentence blurs understanding of the process by which energetic charged particles from the sun interact with the earth's magnetic field and our atmosphere to result in the aurorae.Whenever one hears people speaking of 'energy fields', 'psychic energy', and other expressions treating energy as a 'thing' or 'substance', you know they aren't talking physics, they are talking moonshine.

In certain quack theories of oriental medicine, such as

qi gong(pronouncedchee gung) something calledqiis believed to circulate through the body on specific, mappable pathways calledmeridians. This idea pervades the contrived explanations/rationalizations of acupuncture, and the qiis generally translated into English asenergy. No one has ever found this so-called 'energy', nor confirmed the uniqueness of its meridian pathways, nor verified, through proper double-blind tests, that any therapy or treatment based on the theory actually works. The proponents ofqican't say whether it is a fluid, gas, charge, current, or something else, and their theory requires that it doesn't obey any of the physics of known carriers of energy. But, as soon as we hear someone talking about it as if it were athingwe know they are not talking science, but quackery.

**Equal.** [Not all 'equals' are equal.] The word *equal* and
the symbol '=' have many *different* uses. The dictionary warns that
equal things are 'alike or in agreement in a specified sense with respect
to specified properties.' This we must be careful about the specified
sense and specified properties.

The meaning of the the mathematical symbol, '=' depends upon what stands
on either side of it. When it stands between vectors it symbolizes that
the vectors are equal in both size *and* direction.

In algebra the equal sign stands between two algebraic expressions and indicates that two expressions are related by a reflexive, symmetric and transitive relation. The mathematical expressions on either side of the '=' sign are mathematically identical and interchangeable in equations.

When the equal sign stands between two mathematical expressions with physical meaning, it means something quite different. In physics we may correctly write 12 inches = 1 foot, but to write 12 = 1 is simply wrong. In the first case, the equation tells us about physically equivalent measurements. It has physical meaning, and the units are an indispensable part of the quantity.

When we write **a =** d**v**/dt, we are *defining* the acceleration
in terms of the time rate of change of velocity. One does not verify a
definition by experiment. Experiment can, however, show that in certain cases
(such as a freely falling body) the acceleration of the body is constant.

The three-lined equal sign,When we write=, is often used to mean 'defined equal to'. Unfortunately this symbol is not part of the HTML character set, so in this document we use an underlined equal sign instead.

Additional discussion of these points may be found in Arnold Arons' book
*A Guide to Introductory Physics Teaching*, section 3.23, listed in
the references at the end of this document.

Usage note:Whenreadingequations aloud we often say, 'F equals m a'. This, of course, says that the two things are mathematically equal in equations, and that one may replace the other. It isnotsaying that Fisphysically the same thing as ma. Perhaps equations were not meant to be read aloud, for the spoken word does not have the subtleties of meaning necessary for the task. At least we should realize that spoken equations are at best a shorthand approximation to the meaning; a verbal description of the symbols. If we were to try to speak the physical meaning, it would be something like: 'Newton's law tells us that the net vector force acting on a body of mass m is mathematically equal to the product of its mass and its vector acceleration.' In a textbook, words like that would appear in the text near the equation, at least on the first appearance of the equation.

**Error analysis.** The mathematical analysis done to show
quantitatively how uncertainties in data produce uncertainty in calculated
results, and to find the sizes of the uncertainty in the results. [In
mathematics the word *analysis* is synonymous with *calculus*,
or 'a method for mathematical calculation.' Calculus courses used to be
named *Analysis*.]

See: uncertainty
**Extensive property.** A measurable property
of a thermodynamic system is extensive if, when two identical systems are
combined into one, the value of that property of the combined system is
double its original value in each system. Examples: mass, volume, number
of moles.
See: intensive variable and specific.

**Experimental error.** The uncertainty in the value of a
quantity. This may be found from (1) statistical analysis of the
scatter of data, or (2) mathematical analysis showing how data
uncertainties affect the uncertainty of calculated results.

Misuse alert:In elementary lab manuals one often sees: experimental error = |your value - book value| /book value. Thisshouldbe called theexperimental discrepancy.See: discrepancy.

Misuse alert:Be careful that the reader does not confuse this with the colloquial usage: 'One factor in the success of this experiment was…'

**FPS.** The system of units based on the fundamental units of
the ‘English system’: foot, pound and second.

**Heat.** Heat, like work, is a measure of the amount of energy
*transferred* from one body to another because of the temperature
difference between those bodies. Heat is *not* energy
*possessed* by a body. We should *not* speak of the 'heat
*in* a body.' The energy a body possesses due to its temperature is a
different thing, called *internal thermal energy*. The misuse of
this word
probably dates back to the 18th century when it was still thought that
bodies undergoing thermal processes exchanged a substance, called
*caloric* or *phlogiston*, a substance later called
*heat*. We now know
that heat is not a substance. Reference: Zemansky, Mark W. *The Use
and Misuse of the Word 'Heat' in Physics Teaching'* **The Physics
Teacher, 8**, 6 (Sept 1970) p. 295-300.
See: work.

**Heisenberg's Uncertainty Principle.** Pairs of measurable
quantities whose product has dimensions of energy×time are called
*conjugate quantities* in quantum mechanics, and have a
special relation to each other, expressed in Heisenberg's
uncertainty principle. It says that the product of the
uncertainties of the two quantities is no smaller than h/2. Thus
if you improve the measurement precision of one quantity the
precision of the other gets worse.

Misuse alert:Folks who don't pay attention to details of science, are heard to say 'Heisenberg showed that you can't be certain about anything.' We also hear some folk justifying belief in esp or psychic phenomena by appeal to the Heisenberg principle. This is wrong on several counts. (1) The precision ofanymeasurement is never perfectly certain, and we knew that before Heisenberg. (2) The Heisenberg uncertainty principle tells us we can measure anything with arbitrarily small precision, but in the process someothermeasurement gets worse. (3) The uncertainties involved here affect only microscopic (atomic and molecular level phenomena) and have no applicability to the macroscopic phenomena of everyday life.

**Ideal-lens equation.** *1/p + 1/q = 1/f*, where p is the
distance from object to lens, q is the distance from lens to image,
and f is the focal length of the lens. This equation has important
limitations, being only valid for *thin* lenses, and for
*paraxial rays.* Thin lenses have thickness small compared
to p, q, and f. Paraxial rays are those which make angles small
enough with the optic axis that the approximation
*(angle in radian measure) = sin(angle)* may be used.
See: optical sign conventions,
and image.

**Inertia** A descriptive term for that property of a body which
resists change in its motion. Two kinds of changes of motion are
recognized: changes in translational motion, and changes in rotational
motion.

In modern usage, the measure of translational inertia is mass. Newton's first law of motion is sometimes called the 'Law of Inertia', a label which adds nothing to the meaning of the first law. Newton's first and second laws together are required for a full description of the consequences of a body's inertia.

The measure of a body's resistance to rotation is its *Moment of
Inertia*.

**Inertial frame.** A non-accelerating coordinate system. One in which
* F = ma* holds, where

**Intensive variable.** A measurable property of a thermodynamic
system is intensive if when two identical systems are combined into
one, the variable of the combined system is the same as the
original value in each system. Examples: temperature, pressure.
See: extensive variable, and
specific.

**Image.** (Optics) A surprising number of physics glossaries
omit a definition of this! No wonder. It's difficult to put in a
few words, and still be comprehensive in scope. Try this. **Image:**
A point mapping of luminous points of an object located in one
region of space to points in another region of space, formed by
refraction or reflection of light in a manner which causes light
from each point of the object to converge to or diverge from a
point somewhere else (on the image). The images which are useful
generally have the character that adjacent points of the object map
to adjacent points of the image without discontinuity,
and is a recognizable (though perhaps somewhat distorted) mapping of the
object. See: real image
and virtual image.

**Law.** A statement, usually mathematical, which describes some
physical phenomena.
Compare: hypothesis
and theory.

**Lens.** A transparent object with two refracting surfaces.
Usually the surfaces are flat or spherical (spherical lenses).
Sometimes, to improve image quality. Lenses are deliberately made
with surfaces which depart slightly from spherical (aspheric
lenses).

**Kinetic energy.** The energy a body has by virtue of its
motion. The kinetic energy is the work done by an external force
to bring the body from rest to a particular state of motion.
See: work.

Common misconception:Many students think that kinetic energy isdefinedby½mv. It is not. That happens to be approximately the kinetic energy of objects moving slowly, at small fractions of the speed of light. If the body is moving at relativistic speeds, its kinetic energy is^{2}mc, which can be expressed as^{2}½mv.^{2}+ an infinite series of terms, where^{2}= 1/(1-(v/c)^{2})cis the speed of light in a vacuum.

**Macroscopic.** A physical entity or process of large scale,
the scale of ordinary human experience. Specifically, any phenomena in
which the individual molecules and atoms are neither measured, nor
explicitly considered in the description of the phenomena.
See: microscopic.

**Magnification.**

Two kinds of magnification are useful to describe
optical systems and they must not be confused, since they aren't
synonymous. Any optical system which produces a real image from a real
object is described by its *linear magnification*. Any system
which one looks through to view a virtual image is described by its
*angular magnification*. These have different definitions, and are
based on fundamentally different concepts.

**Linear Magnification** is the ratio of the size of the object to the
size of the image.

**Angular Magnification** is the ratio of the angular size of the
object as seen through the instrument to the angular size of the
object as seen *with the 'naked eye'*. The 'naked eye' view is
*without* use of the optical instrument, but under optimal viewing
conditions.

Certain 'gotchas' lurk here. What are 'optimal' conditions? Usually this means the conditions in which the object's details can be seen most clearly. For a small object held in the hand, this would be when the object is brought as close as possible and still seen clearly, that it, to the near point of the eye, about 25 cm for normal eyesight. For a distant mountain, one can't bring it close, so when determining the magnification of a telescope, we assume the object is very distant, or at infinity.

And what is the 'optimal' position of the image? For the simple magnifier, in which the magnification depends strongly on the image position, the image is best seen at the near point of the eye, 25 cm. For the telescope, the image size doesn't change much as you fiddle with the focus, so you likely will put the image at infinite distance for relaxed viewing. The microscope is an intermediate case. Always striving for greater resolution, the user may pull the image close, to the near point, even though that doesn't increase its size very much. But usually, users will place the image farther away, at the distance of a meter or two, or even at infinity. But, because the object is very near the focal point, the magnification is only weakly dependent on image position.

Some texts express angular magnification as the ratio of the angles, some
express it as the ratio of the tangents of the angles. If all of the
angles are small, there's negligible difference between these two
definitions. However, if you examine the derivation of the formula these
books give for the magnification of a telescope
* f_{o}/f_{e}*, you realize that they must have
been
using the tangents. The tangent form of the definition is the
traditionally correct one, the one used in science and industry, for
nearly all optical instruments which are designed to produce images which
preserve the linear geometry of the object.

**Micro-.** A prefix meaning ‘small’, as in ‘microscope’,
‘micrometer’, ‘micrograph’.
Also, a metric prefix meaning 10^{-6}.
See: macro-

**Microscopic.** A physical entity or process of small scale,
too small to directly experience with our senses. Specifically, any
phenomena on the molecular and atomic scale, or smaller.
See: macroscopic.

**MKSA.** The system of physical units based on the fundamental metric
units: meter kilogram, second and ampere.

**Modern physics.** The physics developed since about 1900,
which includes relativity and quantum mechanics.
See: classical physics.

**Mole.** The term *mole* is short for the name
*gram-molar-weight*; it is *not* a shortened form of the word
*molecule*. (However, the word *molecule* does also derive
from the word *molar*.)
See: Avogadro’s constant.

Misuse alert:Many books emphasize that the mole is 'just a number,' a measure of the number of particles in a collection. They say that one can have a mole ofanykind of particles, baseballs, atoms, stars, grains of sand, etc. It doesn't have to be molecules. This is misleading.To say that the mole is 'just a number' is simply wrong, from physical, pedagogical, philosophical and historical points of view. There's no physical significance to a mole of stars or a mole of grains of sand, or a mole of people. The physical significance of the mole as a measure of quantity arises

onlywhen dealing with physical laws about matter on the molecular scale. The only physical and chemicallawswhich use the mole are those dealing with gases, or systems behaving like gases.

One dictionary definition of *molar* is 'Pertaining to a
body of matter as a whole: contrasted with *molecular* and
*atomic*.' The mole is a measure appropriate for a
*macro*scopic amount of material, as contrasted with a
*micro*scopic amount (a few atoms or molecules).
See: mole,
Avogadro's constant,
microscopic,
macroscopic.

**Newton's first and second laws of motion.** **F** =
d(m**v**)/dt.

* F* is the

**Newton's third law of motion.** When body A exerts a force on body B,
then B exerts and equal and opposite force on A. The two forces related by
this law act on *different bodies*. The forces need not be *net*
forces.

**Ohm's law.** *V = IR*, where *V* is the potential across a
circuit element, *I* is the current through it, and *R* is its
resistance. This is **not** a generally applicable definition of
resistance. It is only applicable to *ohmic* resistors, those whose
resistance *R* is constant over the range of interest and V obeys a
strictly linear relation to *I*.

Materials are said to be *ohmic* when *V* depends linearly on
*R*. Metals are ohmic so long as one holds their temperature
constant. But changing the temperature of a metal changes *R*
slightly. Therefore such a device as an electric light bulb increases its
temperature as it warms up, which is why it glows slightly brighter for a
very brief time just after it is turned on.

For non-ohmic resistors, *R* is a function of current and the
definition *R = dV/dI* is far more useful. This is sometimes called
the *dynamic resistance*. Solid state devices such as thermistors are
non-ohmic, and non-linear. A thermistor's resistance decreases as it warms
up, so its dynamic resistance is negative. Tunnel diodes and some
electrochemical processes have a complicated *I-V* curve with a
negative resistance region of operation.

The dependence of resistance on current is partly due to the change in the device's temperature with increasing current, but other subtle processes also contribute to change in resistance in solid state devices.

**Operational definition.** A definition which describes an
*experimental procedure* by which a numeric value of the quantity may
be determined.
See dimensions.

Example:Length is operationally defined by specifying aprocedurefor subdividing a standard of length into smaller units to make a measuring stick, then laying that stick on the object to be measured, etc..

**Optical sign conventions.** In introductory
(freshman) courses in physics a sign convention is used for objects and
images in which the lens equation must be written *1/p + 1/q = 1/f*.
Often the rules for this sign convention are presented in a convoluted
manner. A simple and easy to remember rule is this: *p* is the
*object-to-lens* distance. *q* is the *lens to image*
distance. The coordinate axis along the optic axis is in the direction of
passage of light through the lens, this defining the *positive*
direction. Example: If the axis and the light direction is left-to-right
(as is usually done) and the object is to the left of the lens, the
object-to-lens distance is positive. if the object is to the right of the
lens (virtual object), the object-to-lens distance is negative. It works
the same for images.

For refractive surfaces, define the surface radius to be the directed
distance from a surface to its center of curvature. Thus a surface convex
to the incident light is positive, one concave to the incident light is
negative. The surface equation is then *n/s + n'/s' = (n'-n)/R* where
*s* and *s'* are the object and image distances, and *n*
and *n'* the refractive index of the incident and emergent media,
respectively.

For mirrors, the equation is usually written *1/s + 1/s' = 2/R =
1/f*. A diverging mirror is convex to the incoming light, with negative
*f*. From this fact we conclude that *R* is also negative. This
form of the equation is consistent with that of the lens equation, and the
interpretation of sign of focal length is the same also. But violence is
done to the definition of *R* we used above, for refraction. One can
say that the mirror *folds* the length axis at the mirror, so that
emergent rays to a real image at the left represent a positive value of
*s'*. We are forced also to declare that the mirror also flips the
sign of the surface radius. For reflective surfaces, the radius of
curvature is defined to be the directed distance from a surface to its
center of curvature, *measured with respect to the axis used for the
emergent light.* With this qualification the convention for the signs
of *s'* and *R* is the same for mirrors as for refractive
surfaces.

In advanced optics courses, a **cartesian** sign convention is used in
which all things to the left of the lens are negative, all those to the
right are positive. When this is used, the lens equation must be written
*1/p + 1/f = 1/q*. (The sign of the *1/p* term is opposite that
in the other sign convention). This is a particularly meaningful version,
for *1/p* is the measure of vergence (convergence or divergence) of
the rays as they enter the lens, *1/f* is the amount the lens changes
the vergence, and *1/q* is the vergence of the emergent rays.

**Pascal's Principle of Hydrostatics**. Pascal actually has three
separate principles of hydrostatics. When a textbook refers to
*Pascal's Principle* it should specify which is meant.

**Pascal 1: The pressure at any point in a liquid exerts force equally
in all directions.** This means that an infinitessimal surface area
placed at that point will experience the same force due to pressure no
matter what its orientation.

**Pascal 2: When pressure is changed (increased or decreased) at any
point in a homogenous, incompressible fluid, all other points experience
the same change of pressure.**

Except for minor edits and insertion of the words 'homogenous' and
'incompressible', this is the statement of the principle given in John A.
Eldridge's textbook *College Physics* (McGraw-Hill, 1937). Yet over
half of the textbooks I've checked, including recent ones, omit the
important word 'changed'. Some textbooks add the qualification 'enclosed
fluid'. This gives the false impression that the fluid must be in a closed
container, which isn't a necessary condition of Pascal's principle at
all.

Some of these textbooks do indicate that Pascal's principle applies only to changes in pressure, but do so in the surrounding text, not in the bold, highlighted, and boxed statement of the principle. Students, of course, read the emphasized statement of the principle and not the surrounding text. Few books give any examples of the principle applied to anything other than enclosed liquids. The usual example is the hydraulic press. Too few show that Pascal's principle is derivable in one step from Bernoulli's equation. Therefore students have the false impression that these are independent laws.

**Pascal 3. The hydraulic lever.** The hydraulic jack is a problem in
fluid equilibrium, just as a pulley system is a problem in mechanical
equilibrium (no accelerations involved). It's the static situation in
which a small force on a small piston balances a large force on a large
piston. No change of pressure need be involved here. A constant force on
one piston slowly lifts a different piston with a constant force on it. At
all times during this process the fluid is in near-equilibrium. This
'principle' is no more than an application of the definition of pressure
as *F/A*, the quotient of net force to the area over which the force
acts. However, it also uses the principle that pressure in a fluid is
uniform throughout the fluid at all points of the same height.

This hydraulic jack lifitng process is done at constant speed. If the two
pistons are at different levels, as they usually are in real jacks used
for lifting, there's a pressure difference between the two pistons due to
height difference *(rho)gh*. In textbook examples this is generally
considered small enough to neglect and may not even be mentioned.

Pascal's own discussion of the principle is not concisely stated and can
be misleading if hastily read. See his *On the Equilibrium of
Liquids*, 1663. He inroduces the principle with the example of a
piston as part of an enclosed vessel and considers what happens if a force
is applied to that piston. He concludes that each portion of the vessel
is pressed in proportion to its area. He does mention parenthetically that
he is 'excluding the weight of the water..., for I am speaking only of the
piston's effect.'

**Percentage.** Older dictionaries suggested that *percentage* be
used when a non-quantitative statement is being made: 'The percentage
growth of the economy was encouraging.' But use *percent* when
specifying a numerical value: 'The gross national product increased by 2
percent last year.' Though newer dictionaries are more permissive, I find
the indiscriminate and unnecessary use of the ugly word *percentage*
to be overdone and annoying, as in 'The experimental percentage
uncertainty was 9%.' Much more graceful is: 'The experimental uncertainty
was 9%.'

Related note: Students have the strange idea that results are
*better* when expressed as percents. Some experimental
uncertainties must *not* be expressed as percents. Examples: (1)
temperature in Celsius or Fahrenheit measure, (2) index of refraction, (3)
dielectric constants. These measurables have arbitrarily chosen ‘fixed
points’. Consider a 1 degree uncertainty in a temperature of 99 degrees C.
Is the uncertainty 1%? Consider the same error in a measurement of 5
degrees. Is the uncertainty now 20%? Consider how much smaller the percent
would be if the temperature were expressed in degrees Kelvin. This shows
that percent uncertainty of Celsius and Fahrenheit temperature
measurements is meaningless. However, the absolute (Kelvin) temperature
scale has a physically meaningful fixed point (absolute zero), rather than
an arbitrarily chosen one, and in some situations a percent uncertainty of
an absolute temperature *is* meaningful.

**Per unit.** In my opinion this expression is a barbarism best
avoided. When a student is told that electric field is *force per
unit charge* and in the MKS system one unit of charge is a coulomb
(a *huge* amount) must we obtain that much charge to measure
the field? Certainly not. In fact, one must take the limit of
**F**/q as q goes to zero. Simply say: 'Force divided by charge'
or 'F over q' or even 'force per charge'. Unfortunately there is
no graceful way to say these things, other than simply writing the
equation.

*Per* is one of those frustrating words in English. The
*American Heritage Dictionary* definition is: 'To, for, or by
each; for every.' Example: '40 cents per gallon.' We must put
the blame for *per unit* squarely on the scientists and
engineers.

**Precise.** Sharply or clearly defined. Having small experimental
uncertainty. A precise measurement may still be inaccurate, if there were
an unrecognized determinate error in the measurement (for example, a
miscalibrated instrument). Compare: accurate.

**Proof.** A term from logic and mathematics describing an argument
from premise to conclusion using strictly logical principles. In
mathematics, theorems or propositions are established by logical arguments
from a set of axioms, the process of establishing a theorem being called a
*proof*.

The colloquial meaning of ‘proof’ causes lots of problems in physics
discussion and is best avoided. Since mathematics is such an important
part of physics, the mathematician’s meaning of proof should be the only
one we use. Also, we often ask students in upper level courses to do
proofs of certain theorems of mathematical physics, and we are *not*
asking for experimental demonstration!

So, in a laboratory report, we should not say 'We proved Newton's law.'
Rather say, 'Today we *demonstrated* (or *verified*) the
validity of Newton's law in the particular case of…'

**Radioactive material.** A material whose nuclei spontaneously give
off nuclear radiation. Naturally radioactive materials (found in the
earth's crust) give off alpha, beta, or gamma particles. Alpha particles
are Helium nuclei, beta particles are electrons, and gamma particles are
high energy photons.

**Radioactive.** A word distinguishing radioactive materials
from those which aren't. Usage: 'U-235 is radioactive; He-4 is not.'

Note:Radioactiveis least misleading when used as an adjective, not as a noun. It is sometimes used in the noun form as an shortened stand-in forradioactive material, as in the example above.

Misuse alert:Radioactivity is aprocess, not athing, and not asubstance. It is just as incorrect to say 'U-235 emits radioactivity' as it is to say 'current flows.' A malfunctioning nuclear reactor does notrelease radioactivity, though it mayrelease radioactive materialsinto the surrounding environment. A patient being treated by radiation therapy does notabsorb radioactivity, but does absorb some of theradiation(alpha, beta, gamma) given off by the radioactive materials being used.This misuse of the word

radioactivitycauses many people to incorrectly think of radioactivity as something one cangetby being near radioactive materials. There is only one process which behaves anything like that, and it is calledartificially induced radioactivity, a process mainly carried out in research laboratories. When some materials are bombarded with protons, neutrons, or other nuclear particles of appropriate energy, their nuclei may be transmuted, creating unstable isotopes which are radioactive.

In physics the comparison is generally made by taking a quotient. Thus speed is defined to be the dx/dt, the ‘time rate of change of position’.

Common misuse: We often hear non-scientists say such things as 'The car was going at a high rate of speed.' This is redundant at best, since it merely means 'The car was moving at high speed.' It is the sort of mistake made by people who don't think while they talk.

**Reaction.** Reaction forces are those equal and opposite forces of
Newton's Third Law. Though they are sometimes called an *action and
reaction* pair, one never sees a single force referred to as an
*action force*.
See: Newton’s Third Law.

**Real force.** See: inertial
frame.

**Real image.** The point(s) to which light rays converge as
they emerge from a lens or mirror.
See: virtual image.

**Real object.** The point(s) from which light rays diverge as
they enter a lens or mirror.
See: virtual object.

**Relative.** Colloquially 'compared to'. In the *theory of
relativity* observations of moving observers are quantitatively
compared. These observers obtain different values when
measuring the same quantities, and these quantities are said to be
*relative.* The theory, however, shows us how the differing
measured values are precisely related to the relative velocity
of the two observers. Some quantities are found to be the same for
all observers, and are called *invariant.* One postulate of
relativity theory is that the speed of light is an invariant
quantity. When the theory is expressed in four dimensional form,
with the appropriate choice of quantities, new invariant quantities
emerge: the world-displacement *(x + y + z +ict)*, the
energy-momentum four-vector, and the electric and magnetic
potentials may be combined into an invariant four-vector. Thus relativity
theory might properly be called *invariance theory.*

Misuse alert:One hears some folks with superficial minds say 'Einstein showed that everything is relative.' In fact, special relativity shows that only certain measurable things are relative, but in a precisely and mathematically specific way, and other things are,notrelative, for all observers agree on them.

**Scale-limited.** A measuring instrument is said to be
*scale-limited* if the experimental uncertainty in that instrument is
smaller than the smallest division readable on its scale. Therefore the
experimental uncertainty is taken to be half the smallest readable
increment on the scale.

**Specific.** In physics and chemistry the word *specific* in
the name of a quantity usually means ‘divided by an extensive
measure that is, divided by a quantity representing an amount of
material. *Specific volume* means volume divided by mass, which is
the reciprocal of the density. *Specific heat capacity* is the heat
capacity divided by the mass.
See: extensive,
and capacity.

**Tele-.** A prefix meaning *at a distance*, as in
*telescope*, *telemetry*, *television*.

**Term.** One of several quantities which are added together.

Confusion can arise with another use of the word, as when one is asked to “Express the result in terms of mass and time.” This means “as a function of mass and time,” obviously it doesn’t mean that mass and time are to be added as terms.

**Truth.** This is a word best avoided entirely in physics
except when placed in quotes, or with careful qualification. Its
colloquial use has so many shades of meaning from ‘it seems to be
correct’ to the absolute truths claimed by religion, that it’s use
causes nothing but misunderstanding. Someone once said 'Science
seeks proximate (approximate) truths.' Others speak of
*provisional* or *tentative* truths. Certainly science
claims no final or absolute truths.

**Theoretical.** Describing an idea which is part of a theory,
or a consequence derived from theory.

Misuse alert:Do not call an authoritative or ‘book’ value of a physical quantity atheoreticalvalue, as in: 'We compared our experimentally determined value of index of refraction with the theoretical value and found they differed by 0.07.' The value obtained from index of refraction tables comesnotfrom theory, but from experiment, and therefore should not be calledtheoretical.The wordtheoreticallysuffers the same abuse. Only when a numeric valueisa prediction from theory, can one properly refer to it as a 'theoretical value'.

**Uncertainty.** Synonym: *error.* A
measure of the the inherent variability of repeated measurements of a
quantity. A prediction of the probable variability of a result, based on
the inherent uncertainties in the data, found from a mathematical
calculation of how the data uncertainties would, in combination, lead to
uncertainty in the result. This calculation or process by which one
predicts the size of the uncertainty in results from the uncertainties in
data and procedure is called *error analysis.*

See: absolute uncertainty and relative uncertainty.
Uncertainties are always present; the experimenter’s job is to keep them
as small as required for a useful result. We recognize two kinds of
uncertainties: *indeterminate* and *determinate.* Indeterminate
uncertainties are those whose size and sign are unknown, and are sometimes
(misleadingly) called *random*. Determinate uncertainties are those
of definite sign, often referring to uncertainties due to instrument
miscalibration, bias in reading scales, or some unknown influence on the
measurement.

**Units.** Labels which distinguish one type of measurable quantity from
other types. Length, mass and time are distinctly different physical
quantities, and therefore have different unit names, meters, kilograms and
seconds. We use several systems of units, including the metric (SI) units,
the English (or U.S. customary units) , and a number of others of mainly
historical interest.

Note: Some dimensionless quantities are assigned unit names, some are not. Specific gravity has no unit name, but density does. Angles are dimensionless, but have unit names: degree, radian, grad. Some quantities which are physically different, and have different unit names, may have the same dimensions, for example, torque and work. Compare: dimensions.

**Virtual image.** The point(s) from which light rays converge as they
emerge from a lens or mirror. The rays do not actually pass through each
image point, but diverge from it.
See: real image.

**Virtual object.** The point(s) to which light rays converge as they
enter a lens. The rays pass through each object point.
See: real object.

**Weight.** The size of the external force required to keep a body at
rest in its frame of reference.

Elementary textbooks almost universally define weight to be 'the size of
the gravitational force on a body.' This would be fine if they would only
consistently stick to that definition. But, no, they later speak of
*weightless astronauts*, *loss of weight* of a body immersed
in a liquid, etc.

This glossary is created by Donald E. Simanek, Lock Haven University and posted here with permission.

'There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved such a leap. The important thing is not to stop questioning.'

**Albert Einstein**

(*1879-1955*)

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