Test Bank for Small Business An Entrepreneurs Business Plan 9th

Edition Hiduke and Ryan 1285169956 9781285169958

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Chapter 2—Spotting Trends and Opportunities

TRUE/FALSE

1. It is impossible to start a successful business with only a small capital investment.

ANS: F PTS: 1 REF: p. 27

2. Once you have developed a successful business formula you don’t need to worry about revising your
plan.

ANS: F PTS: 1 REF: p. 27

3. Reading magazines and bestsellers in a good way to gather helpful information for starting your
business.

ANS: T PTS: 1 REF: p. 28

4. Technology is an environmental variable.

ANS: T PTS: 1 REF: p. 29

5. Futurist magazine predicts that textbooks may be replaced with online social gaming.

ANS: T PTS: 1 REF: p. 31

 6. In terms of number of households, the number of traditional married with children families is
increasing.

ANS: F PTS: 1 REF: p. 32

7. In 2011, 75% of our GDP was generated through service businesses.

ANS: F PTS: 1 REF: p. 33

8. Generation Y individuals will have 2 -3 different careers in their lives.

ANS: F PTS: 1 REF: p. 34

9. Most of the population increase expected in the U.S. over the next 40 years will be due to immigration.

ANS: T PTS: 1 REF: p. 34

10. Baby boomers are redefining aging and retirement.

ANS: T PTS: 1 REF: p. 36

11. Past generations accurately reflect the buying habits of the baby boomer generation.

ANS: F PTS: 1 REF: p. 37

12. The fastest growing segment of the population is those under 15.

ANS: F PTS: 1 REF: p. 38

13. The iGeneration doesn’t have much influence over the purchasing that occurs in the United States.

ANS: F PTS: 1 REF: p. 41

14. Patti Moir’s Build Your Future, Inc. office is a computer and Internet free zone.

ANS: T PTS: 1 REF: p. 41

15. The middle class is expanding in America today.

ANS: F PTS: 1 REF: p. 42

16. Ethnic diversity is rapidly expanding throughout the United States.

ANS: T PTS: 1 REF: p. 43

17. The number of multigenerational households in the United States is declining.

ANS: F PTS: 1 REF: p. 43

18. When looking for opportunities, a good question to ask your friends is, “What frustrates you most
about your daily life?”

ANS: T PTS: 1 REF: p. 45

19. American’s spend a lower percentage of our income on health care now than in 1950.

ANS: F PTS: 1 REF: p. 45

20. In the United States there is some backlash against technology and social media stirring.

ANS: T PTS: 1 REF: p. 48

21. The MIT Media Lab Research Group studies how to give computers human-like intuition.

ANS: T PTS: 1 REF: p. 48

22. Secondary research is conducted by personal interview.

ANS: F PTS: 1 REF: p. 50

23. Trade associations are a good source of industry data.

ANS: T PTS: 1 REF: p. 51

24. Magazine media kits provide statistics about their readers.

ANS: T PTS: 1 REF: p. 51

25. Media kits will not give you demographic or psychographic information.

ANS: F PTS: 1 REF: p. 51

26. The Directory of Periodicals is a good place to start primary research.

ANS: F PTS: 1 REF: p. 54

27. Primary research involves interacting with the world directly.

ANS: T PTS: 1 REF: p. 54

28. New Eyes research provides a variety of fresh ways to look at a business.

ANS: T PTS: 1 REF: p. 55

29. A Business Plan begins with the industry overview.

ANS: T PTS: 1 REF: p. 55

30. Brainstorming involves setting strict rules on content.

ANS: F PTS: 1 REF: p. 57

31. If entering a market in the embryo stage, be ready to meet and beat the competition head on.

ANS: F PTS: 1 REF: p. 58

 32. Trends usually develop overnight.

ANS: F PTS: 1 REF: p. 60

MULTIPLE CHOICE

1. Which of the following is false?

a. Apple Computer started with $13,500.00
b. Dell Computers started with $1,000.00
c. Nike started with $1,000.00
d. Walt Disney started in his garage
ANS: A PTS: 1 REF: p. 27

2. Which of the following is not one of the five major environmental variables?
a. Price
b. Competition
c. Social/Cultural
d. Legal/Political
ANS: A PTS: 1 REF: p. 30

3. Which of the following characteristics describe today's changing family?

a. More households headed by women
b. People having children later in life
c. More people remarrying and forming blended families
d. All of the above
ANS: D PTS: 1 REF: p. 32

4. Which statement accurately reflects the baby boomer generation?

a. They control over 70% of the financial assets in the United States
b. On average 1,000 baby boomers a day turn 65
c. They control less than half of the nation's discretionary income
d. All of the above.
ANS: A PTS: 1 REF: p. 36
5. are entering entrepreneurship at the highest rate of any age group.

a. Millenials
b. Generation Y
c. Baby Boomers
d. Echo Boomers
ANS: C PTS: 1 REF: p. 39

6. The middle class:

a. Has average debt equal to 50% of their annual income
b. Have incomes stagnated at the 1977 level
c. Has seen their net worth remain unchanged over the last five years
d. All of the above
 ANS: B PTS: 1 REF: p. 42

7. Approximately what percentage of children in this country are being raised by grandparents or other
relatives?
a. 9.5%
b. 2.5%
c. 4.4%
d. 6%
ANS: A PTS: 1 REF: p. 43

8. A major growing segment of the United States population is:

a. Healthy, active 90 year olds
b. Middle class Hispanics
c. Both of the above
d. None of the above
ANS: C PTS: 1 REF: p. 43

9. Which of the following is not an example of Entrepreneur Magazine's top 10 new Franchises for 2012?
a. Dunkin’ Donuts
b. Yogurtland
c. CPR-Cell Phone Repair
d. Smashburger
ANS: A PTS: 1 REF: p. 44

10. When compared to 1950, today Americans spent:

a. About the same percentage of their income on healthcare
b. Approximately 15% more of their income on healthcare
c. Approximately 22% more of the income on healthcare
d. Approximately 8% less of their income on healthcare
ANS: B PTS: 1 REF: p. 45

11. In Sherry Turkle’s new book she explores the growing human tendency to:
a. Rely more and more on each other
b. Depend upon ourselves instead of other people
c. Depend upon ourselves instead of technology
d. Rely on technology above human interactions
ANS: D PTS: 1 REF: p. 48

12. Secondary research:

a. Should be completed after primary research
b. Is another term for “new eyes” research
c. Includes reading what someone else has discovered and published
d. All of the above
ANS: C PTS: 1 REF: p. 50

13. When doing industry research:

a. Only contact trade associations for your industry
b. Contact trade associations for your industry and those your customers might belong to
c. Contact trade associations for your industry and those your customers and suppliers might
Another document from Scribd.com that is
random and unrelated content:
the important step which he made in optical science, by the
establishment of the true doctrine of refractive dispersion.
30
This latter fact has, however, been denied by other experimenters.

[2nd Ed.] [After a careful re-consideration of Sir D. Brewster’s

asserted analysis of the solar light into three colors by means of 66
absorbing media, I cannot consider that he has established his point as an
exception to Newton’s doctrine. In the first place, the analysis of light
into three colors appears to be quite arbitrary, granting all his
experimental facts. I do not see why, using other media, he might not just
as well have obtained other elementary colors. In the next place, this
cannot be called an analysis in the same sense as Newton’s analysis,
except the relation between the two is shown. Is it meant that Newton’s
experiments prove nothing? Or is Newton’s conclusion allowed to be
true of light which has not been analysed by absorption? And where are
we to find such light, since the atmosphere absorbs? But, I must add, in
the third place, that with a very sincere admiration of Sir D. Brewster’s
skill as an experimenter, I think his experiment requires, not only
limitation, but confirmation by other experimenters. Mr. Airy repeated
the experiments with about thirty different absorbing substances, and
could not satisfy himself that in any case they changed the color of a ray
of given refractive power. These experiments were described by him at a
meeting of the Cambridge Philosophical Society.]

We now proceed to the corrections which the next generation

introduced into the details of this doctrine.
 CHAPTER IV.

D A .

T HE discovery that the laws of refractive dispersion of different

substances were such as to allow of combinations which neutralised
the dispersion without neutralizing the refraction, is one which has
hitherto been of more value to art than to science. The property has no
definite bearing, which has yet been satisfactorily explained, upon the
theory of light; but it is of the greatest importance in its application to the
construction of telescopes; and it excited the more notice, in
consequence of the prejudices and difficulties which for a time retarded
the discovery.

Newton conceived that he had proved by experiment, 31 that light 67 is

white after refraction, when the emergent rays are parallel to the incident,
and in no other case. If this were so, the production of colorless images
by refracting media would be impossible; and such, in deference to
Newton’s great authority, was for some time the general persuasion.
Euler 32 observed, that a combination of lenses which does not color the
image must be possible, since we have an example of such a
combination in the human eye; and he investigated mathematically the
conditions requisite for such a result. Klingenstierna, 33 a Swedish
mathematician, also showed that Newton’s rule could not be universally
true. Finally, John Dollond, 34 in 1757, repeated Newton’s experiment,
and obtained an opposite result. He found that when an object was seen
through two prisms, one of glass and one of water, of such angles that it
did not appear displaced by refraction, it was colored. Hence it followed
that, without being colored, the rays might be made to undergo
refraction; and that thus, substituting lenses for prisms, a combination
might be formed, which should produce an image without coloring it,
and make the construction of an achromatic telescope possible.
31
Opticks, B. i. p. ii. Prop. 3.
 32
Ac. Berlin. 1747.

33
Swedish Trans. 1754.

34
Phil. Trans. 1758.

Euler at first hesitated to confide in Dollond’s experiments; but he was

assured of their correctness by Clairaut, who had throughout paid great
attention to the subject; and those two great mathematicians, as well as
D’Alembert, proceeded to investigate mathematical formulæ which
might be useful in the application of the discovery. The remainder of the
deductions, which were founded upon the laws of dispersion of various
refractive substances, belongs rather to the history of art than of science.
Dollond used at first, for his achromatic object-glass, a lens of crown-
glass, and one of flint-glass. He afterwards employed two lenses of the
former substance, including between them one of the latter, adjusting the
curvatures of his lenses in such a way as to correct the imperfections
arising from the spherical form of the glasses, as well as the fault of
color. Afterwards, Blair used fluid media along with glass lenses, in
order to produce improved object-glasses. This has more recently been
done in another form by Mr. Barlow. The inductive laws of refraction
being established, their results have been deduced by various
mathematicians, as Sir J. Herschel and Professor Airy among ourselves,
who have simplified and extended the investigation of the formulæ
which determine the best combination of lenses in the object-glasses and
eye-glasses of 68 telescopes, both with reference to spherical and to
chromatic aberrations.

According to Dollond’s discovery, the colored spectra produced by

prisms of two substances, as flint-glass and crown-glass, would be of the
same length when the refraction was different. But a question then
occurred: When the whole distance from the red to the violet in one
spectrum was the same as the whole distance in the other, were the
intermediate colors, yellow, green, &c., in corresponding places in the
two? This point also could not be determined any otherwise than by
experiment. It appeared that such a correspondence did not exist; and,
therefore, when the extreme colors were corrected by combinations of
the different media, there still remained an uncorrected residue of color
arising from the rest of the spectrum. This defect was a consequence of
the property, that the spectra belonging to different media were not
divided in the same ratio by the same colors, and was hence termed the
irrationality of the spectrum. By using three prisms, or three lenses, three
colors may be made to coincide instead of two, and the effects of this
irrationality greatly diminished.

For the reasons already mentioned, we do not pursue this subject

further, 35 but turn to those optical facts which finally led to a great and
comprehensive theory.
35
The discovery of the fixed lines in the spectrum, by Wollaston and
Fraunhofer, has more recently supplied the means of determining, with
extreme accuracy, the corresponding portions of the spectrum in different
refracting substances.

[2nd Ed.] [Mr. Chester More Hall, of More Hall, in Essex, is said to
have been led by the study of the human eye, which he conceived to be
achromatic, to construct achromatic telescopes as early as 1729. Mr.
Hall, however, kept his invention a secret. David Gregory, in his
Catoptrics (1713), had suggested that it would perhaps be an
improvement of telescopes, if, in imitation of the human eye, the object-
glass were composed of different media. Encyc. Brit. art. Optics.

It is said that Clairaut first discovered the irrationality of the colored

spaces in the spectrum. In consequence of this irrationality, it follows
that when two refracting media are so combined as to correct each
other’s extreme dispersion, (the separation of the red and violet rays,)
this first step of correction still leaves a residue of 69 coloration arising
from the unequal dispersion of the intermediate rays (the green, &c.).
These outstanding colors, as they were termed by Professor Robison,
form the residual, or secondary spectrum.
 Dr. Blair, by very ingenious devices, succeeded in producing an
object-glass, corrected by a fluid lens, in which this aberration of color
was completely corrected, and which performed wonderfully well.

The dispersion produced by a prism may be corrected by another

prism of the same substance and of a different angle. In this case also
there is an irrationality in the colored spaces, which prevents the
correction of color from being complete; and hence, a new residuary
spectrum, which has been called the tertiary spectrum, by Sir David
Brewster, who first noticed it.

I have omitted, in the notice of discoveries respecting the spectrum,

many remarkable trains of experimental research, and especially the
investigations respecting the power of various media to absorb the light
of different parts of the spectrum, prosecuted by Sir David Brewster with
extraordinary skill and sagacity. The observations are referred to in
chapter iii. Sir John Herschel, Prof. Miller, Mr. Daniel, Dr. Faraday, and
Mr. Talbot, have also contributed to this part of our knowledge.]
 CHAPTER V.

D L D R .

T HE laws of refraction which we have hitherto described, were simple

and uniform, and had a symmetrical reference to the surface of the
refracting medium. It appeared strange to men, when their attention was
drawn to a class of phenomena in which this symmetry was wanting, and
in which a refraction took place which was not even in the plane of
incidence. The subject was not unworthy the notice and admiration it
attracted; for the prosecution of it ended in the discovery of the general
laws of light. The phenomena of which I now speak, are those exhibited
by various kinds of crystalline bodies; but observed for a long time in
one kind only, namely, the rhombohedral calc-spar; or, as it was usually
termed, from the country which supplied the largest and clearest crystals,
Iceland spar. These 70 rhombohedral crystals are usually very smooth
and transparent, and often of considerable size; and it was observed, on
looking through them, that all objects appeared double. The phenomena,
even as early as 1669, had been considered so curious, that Erasmus
Bartholin published a work upon them at Copenhagen, 36 (Experimenta
Crystalli Islandici, Hafniæ, 1669.) He analysed the phenomena into their
laws, so far as to discover that one of the two images was produced by
refraction after the usual rule, and the other by an unusual refraction.
This latter refraction Bartholin found to vary in different positions; to be
regulated by a line parallel to the sides of the rhombohedron; and to be
greatest in the direction of a line bisecting two of the angles of the
rhombic face of the crystal.
36
Priestley’s Optics, p. 550.

These rules were exact as far as they went; and when we consider how
geometrically complex the law is, which really regulates the unusual or
extraordinary refraction;—that Newton altogether mistook it, and that it
was not verified till the experiments of Haüy and Wollaston in our own
time;—we might expect that it would not be soon or easily detected. But
Huyghens possessed a key to the secret, in the theory, which he had
devised, of the propagation of light by undulations, and which he
conceived with perfect distinctness and correctness, so far as its
application to these phenomena is concerned. Hence he was enabled to
lay down the law of the phenomena (the only part of his discovery which
we have here to consider), with a precision and success which excited
deserved admiration, when the subject, at a much later period, regained
its due share of attention. His Treatise was written 37 in 1678, but not
published till 1690.
37
See his Traité de la Lumière. Preface.

The laws of the ordinary and the extraordinary refraction in Iceland

spar are related to each other; they are, in fact, similar constructions,
made, in the one case, by means of an imaginary sphere, in the other, by
means of a spheroid; the spheroid being of such oblateness as to suit the
rhombohedral form of the crystal, and the axis of the spheroid being the
axis of symmetry of the crystal. Huyghens followed this general
conception into particular positions and conditions; and thus obtained
rules, which he compared with observation, for cutting the crystal and
transmitting the rays in various manners. “I have examined in detail,”
says he, 38 “the properties of the 71 extraordinary refraction of this
crystal, to see if each phenomenon which is deduced from theory, would
agree with what is really observed. And this being so, it is no slight proof
of the truth of our suppositions and principles; but what I am going to
add here confirms them still more wonderfully; that is, the different
modes of cutting this crystal, in which the surfaces produced give rise to
refractions exactly such as they ought to be, and as I had foreseen them,
according to the preceding theory.”
38
See Maseres’s Tracts on Optics, p. 250; or Huyghens, Tr. sur la Lum. ch. v.
Art. 43.

Statements of this kind, coming from a philosopher like Huyghens,

were entitled to great confidence; Newton, however, appears not to have
noticed, or to have disregarded them. In his Opticks, he gives a rule for
the extraordinary refraction of Iceland spar which is altogether
erroneous, without assigning any reason for rejecting the law published
by Huyghens; and, so far as appears, without having made any
experiments of his own. The Huyghenian doctrine of double refraction
fell, along with his theory of undulations, into temporary neglect, of
which we shall have hereafter to speak. But in 1788, Haüy showed that
Huyghens’s rule agreed much better than Newton’s with the phenomena:
and in 1802, Wollaston, applying a method of his own for measuring
refraction, came to the same result. “He made,” says Young, 39 “a number
of accurate experiments with an apparatus singularly well calculated to
examine the phenomena, but could find no general principle to connect
them, until the work of Huyghens was pointed out to him.” In 1808, the
subject of double refraction was proposed as a prize-question by the
French Institute; and Malus, whose Memoir obtained the prize, says, “I
began by observing and measuring a long series of phenomena on
natural and artificial faces of Iceland spar. Then, testing by means of
these observations the different laws proposed up to the present time by
physical writers, I was struck with the admirable agreement of the law of
Huyghens with the phenomena, and I was soon convinced that it is really
the law of nature.” Pursuing the consequences of the law, he found that it
satisfied phenomena which Huyghens himself had not observed. From
this time, then, the truth of the Huyghenian law was universally allowed,
and soon afterwards, the theory by which it had been suggested was
generally received.
39
Quart. Rev. 1809, Nov. p. 338.

The property of double refraction had been first studied only in

Iceland spar, in which it is very obvious. The same property belongs, 72
though less conspicuously, to many other kinds of crystals. Huyghens
had noticed the same fact in rock-crystal; 40 and Malus found it to belong
to a large list of bodies besides; for instance, arragonite, sulphate of lime,
of baryta, of strontia, of iron; carbonate of lead; zircon, corundum,
cymophane, emerald, euclase, felspar, mesotype, peridote, sulphur, and
mellite. Attempts were made, with imperfect success, to reduce all these
to the law which had been established for Iceland spar. In the first
instance, Malus took for granted that the extraordinary refraction
depended always upon an oblate spheroid; but M. Biot 41 pointed out a
distinction between two classes of crystals in which this spheroid was
oblong and oblate respectively, and these he called attractive and
repulsive crystals. With this correction, the law could be extended to a
considerable number of cases; but it was afterwards proved by Sir D.
Brewster’s discoveries, that even in this form, it belonged only to
substances of which the crystallization has relation to a single axis of
symmetry, as the rhombohedron, or the square pyramid. In other cases,
as the rhombic prism, in which the form, considered with reference to its
crystalline symmetry, is biaxal, the law is much more complicated. In
that case, the sphere and the spheroid, which are used in the construction
for uniaxal crystals, transform themselves into the two successful
convolutions of a single continuous curve surface; neither of the two rays
follows the law of ordinary refraction; and the formula which determines
their position is very complex. It is, however, capable of being tested by
measures of the refractions of crystals cut in a peculiar manner for the
purpose, and this was done by MM. Fresnel and Arago. But this complex
law of double refraction was only discovered through the aid of the
theory of a luminiferous ether, and therefore we must now return to the
other facts which led to such a theory.
40
Traité de la Lumière, ch. v. Art. 20

41
Biot, Traité de Phys. iii. 330.
 CHAPTER VI.

D L P .

I F the Extraordinary Refraction of Iceland spar had appeared strange,

another phenomenon was soon noticed in the same 73 substance,
which appeared stranger still, and which in the sequel was found to be no
less important. I speak of the facts which were afterwards described
under the term Polarization. Huyghens was the discoverer of this class of
facts. At the end of the treatise which we have already quoted, he says, 42
“Before I quit the subject of this crystal, I will add one other marvellous
phenomenon, which I have discovered since writing the above; for
though hitherto I have not been able to find out its cause, I will not, on
that account, omit pointing it out, that I may give occasion to others to
examine it.” He then states the phenomena; which are, that when two
rhombohedrons of Iceland spar are in parallel positions, a ray doubly
refracted by the first, is not further divided when it falls on the second:
the ordinarily refracted ray is ordinarily refracted only, and the
extraordinary ray is only extraordinarily refracted by the second crystal,
neither ray being doubly refracted. The same is still the case, if the two
crystals have their principal planes parallel, though they themselves are
not parallel. But if the principal plane of the second crystal be
perpendicular to that of the first, the reverse of what has been described
takes place; the ordinarily refracted ray of the first crystal suffers, at the
second, extraordinary refraction only, and the extraordinary ray of the
first suffers ordinary refraction only at the second. Thus, in each of these
positions, the double refraction of each ray at the second crystal is
reduced to single refraction, though in a different manner in the two
cases. But in any other position of the crystals, each ray, produced by the
first, is doubly refracted by the second, so as to produce four rays.
42
Tr. Opt. p. 252.

A step in the right conception of these phenomena was made by

Newton, in the second edition of his Opticks (1717). He represented
them as resulting from this;—that the rays of light have “sides,” and that
they undergo the ordinary or extraordinary refraction, according as these
sides are parallel to the principal plane of the crystal, or at right angles to
it (Query 26). In this way, it is clear, that those rays which, in the first
crystal, had been selected for extraordinary refraction, because their
sides were perpendicular to the principal plane, would all suffer
extraordinary refraction at the second crystal for the same reason, if its
principal plane were parallel to that of the first; and would all suffer
ordinary refraction, if the principal plane of the second crystal were
perpendicular to that of the first, and 74 consequently parallel to the sides
of the refracted ray. This view of the subject includes some of the leading
features of the case, but still leaves several considerable difficulties.

No material advance was made in the subject till it was taken up by

Malus, 43 along with the other circumstances of double refraction, about a
hundred years afterwards. He verified what had been observed by
Huyghens and Newton, on the subject of the variations which light thus
exhibits; but he discovered that this modification, in virtue of which light
undergoes the ordinary, or the extraordinary, refraction, according to the
position of the plane of the crystal, may be impressed upon it many other
ways. One part of this discovery was made accidentally. 44 In 1808,
Malus happened to be observing the light of the setting sun, reflected
from the windows of the Luxembourg, through a rhombohedron of
Iceland spar; and he observed that in turning round the crystal, the two
images varied in their intensity. Neither of the images completely
vanished, because the light from the windows was not properly modified,
or, to use the term which Malus soon adopted, was not completely
polarized. The complete polarization of light by reflection from glass, or
any other transparent substance, was found to take place at a certain
definite angle, different for each substance. It was found also that in all
crystals in which double refraction occurred, the separation of the
refracted rays was accompanied by polarization; the two rays, the
ordinary and the extraordinary, being always polarized oppositely, that is,
in planes at right angles to each other. The term poles, used by Malus,
conveyed nearly the same notion as the term sides which had been
employed by Newton, with the additional conception of a property which
appeared or disappeared according as the poles of the particles were or
were not in a certain direction; a property thus resembling the polarity of
magnetic bodies. When a spot of polarized light is looked at through a
transparent crystal of Iceland spar, each of the two images produced by
the double refraction varies in brightness as the crystal is turned round.
If, for the sake of example, we suppose the crystal to be turned round in
the direction of the points of the compass, N, E, S, W, and if one image
be brightest when the crystal marks N and S, it will disappear when the
crystal marks E and W: and on the contrary, the second image will vanish
when the crystal marks N and S, 75 and will be brightest when the crystal
marks E and W. The first of these images is polarized in the plane NS
passing through the ray, and the second in the plane EW, perpendicular
to the other. And these rays are oppositely polarized. It was further found
that whether the ray were polarized by reflection from glass, or from
water, or by double refraction, the modification of light so produced, or
the nature of the polarization, was identical in all these cases;—that the
alternatives of ordinary and extraordinary refraction and non-refraction,
were the same, by whatever crystal they were tested, or in whatever
manner the polarization had been impressed upon the light; in short, that
the property, when once acquired, was independent of everything except
the sides or poles of the ray; and thus, in 1811, the term “polarization”
was introduced. 45
43
Malus, Th. de la Doub. Réf. p. 296.

44
Arago, art. Polarization, Supp. Enc. Brit.

45
Mém. Inst. 1810.

This being the state of the subject, it became an obvious question, by

what other means, and according to what laws, this property was
communicated. It was found that some crystals, instead of giving, by
double refraction, two images oppositely polarized, give a single
polarized image. This property was discovered in the agate by Sir D.
Brewster, and in tourmaline by M. Biot and Dr. Seebeck. The latter
mineral became, in consequence, a very convenient part of the apparatus
used in such observations. Various peculiarities bearing upon this
subject, were detected by different experimenters. It was in a short time
discovered, that light might be polarized by refraction, as well as by
reflection, at the surface of uncrystallized bodies, as glass; the plane of
polarization being perpendicular to the plane of refraction; further, that
when a portion of a ray of light was polarized by reflection, a
corresponding portion was polarized by transmission, the planes of the
two polarizations being at right angles to each other. It was found also
that the polarization which was incomplete with a single plate, either by
reflection or refraction, might be made more and more complete by
increasing the number of plates.

Among an accumulation of phenomena like this, it is our business to

inquire what general laws were discovered. To make such discoveries
without possessing the general theory of the facts, required no ordinary
sagacity and good fortune. Yet several laws were detected at this stage of
the subject. Malus, in 1811, obtained the important generalization that,
whenever we obtain, by any means, a polarized ray of light, we produce
also another ray, polarized in a contrary 76 direction; thus when reflection
gives a polarized ray, the companion-ray is refracted polarized
oppositely, along with a quantity of unpolarized light. And we must
particularly notice Sir D. Brewster’s rule for the polarizing angle of
different bodies.

Malus 46 had said that the angle of reflection from transparent bodies
which most completely polarizes the reflected ray, does not follow any
discoverable rule with regard to the order of refractive or dispersive
powers of the substances. Yet the rule was in reality very simple. In
1815, Sir D. Brewster stated 47 as the law, which in all cases determines
this angle, that “the index of refraction is the tangent of the angle of
polarization.” It follows from this, that the polarization takes place when
the reflected and refracted rays are at right angles to each other. This
simple and elegant rule has been fully confirmed by all subsequent
observations, as by those of MM. Biot and Seebeck; and must be
considered one of the happiest and most important discoveries of the
laws of phenomena in Optics.
46
Mém. Inst. 1810.

47
Phil. Trans. 1815.

The rule for polarization by one reflection being thus discovered,

tentative formulæ were proposed by Sir D. Brewster and M. Biot, for the
cases in which several reflections or refractions take place. Fresnel also
in 1817 and 1818, traced the effect of reflection in modifying the
direction of polarization, which Malus had done inaccurately in 1810.
But the complexity of the subject made all such attempts extremely
precarious, till the theory of the phenomena was understood, a period
which now comes under notice. The laws which we have spoken of were
important materials for the establishment of the theory; but in the mean
time, its progress at first had been more forwarded by some other classes
of facts, of a different kind, and of a longer standing notoriety, to which
we must now turn our attention.
 CHAPTER VII.

D L C T P .

T HE facts which we have now to consider are remarkable, inasmuch

as the colours are produced merely by the smallness of dimensions
of the bodies employed. The light is not analysed by any peculiar 77
property of the substances, but dissected by the minuteness of their parts.
On this account, these phenomena give very important indications of the
real structure of light; and at an early period, suggested views which are,
in a great measure, just.

Hooke appears to be the first person who made any progress in

discovering the laws of the colors of thin plates. In his Micrographia,
printed by the Royal Society in 1664, he describes, in a detailed and
systematic manner, several phenomena of this kind, which he calls
“fantastical colors.” He examined them in Muscovy glass or mica, a
transparent mineral which is capable of being split into the exceedingly
thin films which are requisite for such colors; he noticed them also in the
fissures of the same substance, in bubbles blown of water, rosin, gum,
glass; in the films on the surface of tempered steel; between two plane
pieces of glass; and in other cases. He perceived also, 48 that the
production of each color required a plate of determinate thickness, and
he employed this circumstance as one of the grounds of his theory of
light.
48
Micrographia, p. 53.

Newton took up the subject where Hooke had left it; and followed it
out with his accustomed skill and clearness, in his Discourse on Light
and Colors, communicated to the Royal Society in 1675. He determined,
what Hooke had not ascertained, the thickness of the film which was
requisite for the production of each color; and in this way explained, in a
complete and admirable manner, the colored rings which occur when two
lenses are pressed together, and the scale of color which the rings follow;
a step of the more consequence, as the same scale occurs in many other
optical phenomena.

It is not our business here to state the hypothesis with regard to the
properties of light which Newton founded on these facts;—the “fits of
easy transmission and reflection.” We shall see hereafter that his
attempted induction was imperfect; and his endeavor to account, by
means of the laws of thin plates, for the colors of natural bodies, is
altogether unsatisfactory. But notwithstanding these failures in the
speculations on this subject, he did make in it some very important steps;
for he clearly ascertained that when the thickness of the plate was about
1
⁄178000th of an inch, or three times, five times, seven times that magnitude,
there was a bright color produced; but blackness, when the thickness was
exactly intermediate between those magnitudes. He found, also, that the
thicknesses which gave red and 78 violet 49 were as fourteen to nine; and
the intermediate colors of course corresponded to intermediate
thicknesses, and therefore, in his apparatus, consisting of two lenses
pressed together, appeared as rings of intermediate sizes. His mode of
confirming the rule, by throwing upon this apparatus differently colored
homogeneous light, is striking and elegant. “It was very pleasant,” he
says, “to see the rings gradually swell and contract as the color of the
light was changed.”
49
Opticks, p. 184.

It is not necessary to enter further into the detail of these phenomena,

or to notice the rings seen by transmission, and other circumstances. The
important step made by Newton in this matter was, the showing that the
rays of light, in these experiments, as they pass onwards go periodically
through certain cycles of modification, each period occupying nearly the
small fraction of an inch mentioned above; and this interval being
different for different colors. Although Newton did not correctly
disentangle the conditions under which this periodical character is
manifestly disclosed, the discovery that, under some circumstances, such
a periodical character does exist, was likely to influence, and did
influence, materially and beneficially, the subsequent progress of Optics
towards a connected theory.

We must now trace this progress; but before we proceed to this task,
we will briefly notice a number of optical phenomena which had been
collected, and which waited for the touch of sound theory to introduce
among them that rule and order which mere observation had sought for
in vain.
 CHAPTER VIII.

A L P .

T HE phenomena which result from optical combinations, even of a

comparatively simple nature, are extremely complex. The theory
which is now known accounts for these results with the most curious
exactness, and points out the laws which pervade the apparent confusion;
but without this key to the appearances, it was scarcely possible that any
rule or order should be detected. The undertaking was of 79 the same
kind as it would have been, to discover all the inequalities of the moon’s
motion without the aid of the doctrine of gravity. We will enumerate
some of the phenomena which thus employed and perplexed the
cultivators of optics.

The fringes of shadows were one of the most curious and noted of
such classes of facts. These were first remarked by Grimaldi 50 (1665),
and referred by him to a property of light which he called Diffraction.
When shadows are made in a dark room, by light admitted through a
very small hole, these appearances are very conspicuous and beautiful.
Hooke, in 1672, communicated similar observations to the Royal
Society, as “a new property of light not mentioned by any optical writer
before;” by which we see that he had not heard of Grimaldi’s
experiments. Newton, in his Opticks, treats of the same phenomena,
which he ascribes to the inflexion of the rays of light. He asks (Qu. 3),
“Are not the rays of light, in passing by the edges and sides of bodies,
bent several times backward and forward with a motion like that of an
eel? And do not the three fringes of colored light in shadows arise from
three such bendings?” It is remarkable that Newton should not have
noticed, that it is impossible, in this way, to account for the facts, or even
to express their laws; since the light which produces the fringes must, on
this theory, be propagated, even after it leaves the neighborhood of the
opake body, in curves, and not in straight lines. Accordingly, all who
have taken up Newton’s notion of inflexion, have inevitably failed in
giving anything like an intelligible and coherent character to these
phenomena. This is, for example, the case with Mr. (now Lord)
Brougham’s attempts in the Philosophical Transactions for 1796. The
same may be said of other experimenters, as Mairan 51 and Du Four, 52
who attempted to explain the facts by supposing an atmosphere about the
opake body. Several authors, as Maraldi, 53 and Comparetti, 54 repeated or
varied these experiments in different ways.
50
Physico-Mathesis, de Lumine, Coloribus et Iride. Bologna, 1665.

51
Ac. Par. 1738.

52
Mémoires Présentés, vol. v.

53
Ac. Par. 1723.

54
Observationes Opticæ de Luce Inflexâ et Coloribus. Padua, 1787.

Newton had noticed certain rings of color produced by a glass

speculum, which he called “colors of thick plates,” and which he
attempted to connect with the colors of thin plates. His reasoning is by
no means satisfactory; but it was of use, by pointing out this as a case in
which his “fits” (the small periods, or cycles in the rays of light, of 80
which we have spoken) continued to occur for a considerable length of
the ray. But other persons, attempting to repeat his experiments,
confounded with them extraneous phenomena of other kinds; as the Duc
de Chaulnes, who spread muslin before his mirror, 55 and Dr. Herschel,
who scattered hair-powder before his. 56 The colors produced by the
muslin were those belonging to shadows of gratings, afterwards
examined more successfully by Fraunhofer, when in possession of the
theory. We may mention here also the colors which appear on finely-
striated surfaces, and on mother-of-pearl, feathers, and similar
substances. These had been examined by various persons (as Boyle,
Mazeas, Lord Brougham), but could still, at this period, be only looked
upon as insulated and lawless facts.
55
Ac. Par. 1755.
56
Phil. Trans. 1807.
 CHAPTER IX.

D L P D L .

B ESIDES the above-mentioned perplexing cases of colors produced

by common light, cases of periodical colors produced by polarized
light began to be discovered, and soon became numerous. In August,
1811, M. Arago communicated to the Institute of France an account of
colors seen by passing polarized light through mica, and analysing 57 it
with a prism of Iceland spar. It is remarkable that the light which
produced the colors in this case was the light polarized by the sky, a
cause of polarization not previously known. The effect which the mica
thus produced was termed depolarization;—not a very happy term, since
the effect is not the destruction of the polarization, but the combination
of a new polarizing influence with the former. The word dipolarization,
which has since been proposed, is a much more appropriate expression.
Several other curious phenomena of the same kind were observed in
quartz, and in flint-glass. M. Arago was not able to reduce these
phenomena to laws, but he had a full conviction of their value, and
ventures to class them with the great steps in 81 this part of optics. “To
Bartholin we owe the knowledge of double refraction; to Huyghens, that
of the accompanying polarization; to Malus, polarization by reflection; to
Arago, depolarization.” Sir D. Brewster was at the same time engaged in
a similar train of research; and made discoveries of the same nature,
which, though not published till some time after those of Arago, were
obtained without a knowledge of what had been done by him. Sir D.
Brewster’s Treatise on New Philosophical Instruments, published in
1813, contains many curious experiments on the “depolarizing”
properties of minerals. Both these observers noticed the changes of color
which are produced by changes in the position of the ray, and the
alternations of color in the two oppositely polarized images; and Sir D.
Brewster discovered that, in topaz, the phenomena had a certain
reference to lines which he called the neutral and depolarizing axes. M.
Biot had endeavored to reduce the phenomena to a law; and had
succeeded so far, that he found that in the plates of sulphate of lime, the
place of the tint, estimated in Newton’s scale (see ante, chap. vii.), was
as the square of the sine of the inclination. But the laws of these
phenomena became much more obvious when they were observed by Sir
D. Brewster with a larger field of view. 58 He found that the colors of
topaz, under the circumstances now described, exhibited themselves in
the form of elliptical rings, crossed by a black bar, “the most brilliant
class of phenomena,” as he justly says, “in the whole range of optics.” In
1814, also, Wollaston observed the circular rings with a black cross,
produced by similar means in calc-spar; and M. Biot, in 1815, made the
same observation. The rings in several of these cases were carefully
measured by M. Biot and Sir D. Brewster, and a great mass of similar
phenomena was discovered. These were added to by various persons, as
M. Seebeck, and Sir John Herschel.
57
The prism of Iceland spar produces the colors by separating the
transmitted rays according to the laws of double refraction. Hence it is said to
analyse the light.

58
Phil. Trans. 1814.

Sir D. Brewster, in 1818, discovered a general relation between the

crystalline form and the optical properties, which gave an incalculable
impulse and a new clearness to these researches. He found that there was
a correspondence between the degree of symmetry of the optical
phenomena and the crystalline form; those crystals which are uniaxal in
the crystallographical sense, are also uniaxal in their optical properties,
and give circular rings; those which are of other forms are, generally
speaking, biaxal; they give oval and knotted isochromatic lines, with two
poles. He also discovered a rule for the tint at each point 82 in such cases;
and thus explained, so far as an empirical law of phenomena went, the
curious and various forms of the colored curves. This law, when
simplified by M. Biot, 59 made the tint proportional to the product of the
distances of the point from the two poles. In the following year, Sir J.
Herschel confirmed this law by showing, from actual measurement, that
the curve of the isochromatic lines in these cases was the curve termed
the lemniscata, which has, for each point, the product of the distances
from two fixed poles equal to a constant quantity. 60 He also reduced to
rule some other apparent anomalies in phenomena of the same class.
59
Mém. Inst. 1818, p. 192.

60
Phil. Trans. 1819.

M. Biot, too, gave a rule for the directions of the planes of polarization
of the two rays produced by double refraction in biaxal crystals, a
circumstance which has a close bearing upon the phenomena of
dipolarization. His rule was, that the one plane of polarization bisects the
dihedral angle formed by the two planes which pass through the optic
axes, and that the other is perpendicular to such a plane. When, however,
Fresnel had discovered from the theory the true laws of double
refraction, it appeared that the above rule is inaccurate, although in a
degree which observation could hardly detect without the aid of theory. 61
61
Fresnel, Mém. Inst. 1827, p. 162.

There were still other classes of optical phenomena which attracted

notice; especially those which are exhibited by plates of quartz cut
perpendicular to the axis. M. Arago had observed, in 1811, that this
substance produced a twist of the plane of polarization to the right or left
hand, the amount of this twist being different for different colors; a result
which was afterwards traced to a modification of light different both
from common and from polarized light, and subsequently known as
circular polarization. Sir J. Herschel had the good fortune and sagacity
to discover that this peculiar kind of polarization in quartz was connected
with an equally peculiar modification of crystallization, the plagihedral
faces which are seen, on some crystals, obliquely disposed, and, as it
were, following each other round the crystal from left to right, or from
right to left. Sir J. Herschel found that the right-handed or left-handed
character of the circular polarization corresponded, in all cases, to that of
the crystal.
 In 1815, M. Biot, in his researches on the subject of circular
polarization, was led to the unexpected and curious discovery, that this 83
property which seemed to require for its very conception a crystalline
structure in the body, belonged nevertheless to several fluids, and in
different directions for different fluids. Oil of turpentine, and an essential
oil of laurel, gave the plane of polarization a rotation to the left hand; oil
of citron, syrup of sugar, and a solution of camphor, gave a rotation to
the right hand. Soon after, the like discovery was made independently by
Dr. Seebeck, of Berlin.

It will easily be supposed that all those brilliant phenomena could not
be observed, and the laws of many of the phenomena discovered,
without attempts on the part of philosophers to combine them all under
the dominion of some wide and profound theory. Endeavors to ascend
from such knowledge as we have spoken of, to the general theory of
light, were, in fact, made at every stage of the subject, and with a success
which at last won almost all suffrages. We are now arrived at the point at
which we are called upon to trace the history of this theory; to pass from
the laws of phenomena to their causes;—from Formal to Physical Optics.
The undulatory theory of light, the only discovery which can stand by
the side of the theory of universal gravitation, as a doctrine belonging to
the same order, for its generality, its fertility, and its certainty, may
properly be treated of with that ceremony which we have hitherto
bestowed only on the great advances of astronomy; and I shall therefore
now proceed to speak of the Prelude to this epoch, the Epoch itself, and
its Sequel, according to the form of the preceding Book which treats of
astronomy.

[2nd Ed.] [I ought to have stated, in the beginning of this chapter, that
Malus discovered the depolarization of white light in 1811. He found that
a pencil of light which, being polarized, refused to be reflected by a
surface properly placed, recovered its power of being reflected after
being transmitted through certain crystals and other transparent bodies.
Malus intended to pursue this subject, when his researches were
terminated by his death, Feb. 7, 1812. M. Arago, about the same time,
announced his important discovery of the depolarization of colors by
crystals.

I may add, to what is above said of M. Biot’s discoveries respecting

the circular polarizing power of fluids, that he pursued his researches so
as to bring into view some most curious relations among the elements of
bodies. It appeared that certain substances, as sugar of canes, had a right-
handed effect, and certain other substances, as gum, a left-handed effect;
and that the molecular value of this effect was not altered by dilution. It
appeared also that a certain element of the 84 substance of fruits, which
had been supposed to be gum, and which is changed into sugar by the
operation of acids, is not gum, and has a very energetic right-handed
effect. This substance M. Biot called dextrine, and he has since traced its
effects into many highly curious and important results.]
PHYSICAL OPTICS.
 CHAPTER X.

P E Y F .

B Y Physical Optics we mean, as has already been stated, the theories

which explain optical phenomena on mechanical principles. No such
explanation could be given till true mechanical principles had been
obtained; and, accordingly, we must date the commencement of the
essays towards physical optics from Descartes, the founder of the
modern mechanical philosophy. His hypothesis concerning light is, that
it consists of small particles emitted by the luminous body. He compares
these particles to balls, and endeavors to explain, by means of this
comparison, the laws of reflection and refraction. 62 In order to account
for the production of colors by refraction, he ascribes to these balls an
alternating rotatory motion. 63 This form of the emission theory, was, like
most of the physical speculations of its author, hasty and gratuitous; but
was extensively accepted, like the rest of the Cartesian doctrines, in
consequence of the love which men have for sweeping and simple
dogmas, and deductive reasonings from them. In a short time, however,
the rival optical theory of undulations made its appearance. Hooke in his
Micrographia (1664) propounds it, upon occasion of his observations,
already noticed, (chap. vii.,) on the colors of thin plates. He there
asserts 64 light to consist in a “quick, short, vibrating motion,” and that it
is propagated in a homogeneous medium, in such a way that “every
pulse or vibration of the luminous body will generate a sphere, which
will continually increase and grow bigger, just after the same manner
(though indefinitely swifter) as the waves or rings on the surface of water
do swell into bigger and bigger circles about a point in it.” 65 He applies
this to the explanation of refraction, 86 by supposing that the rays in a
denser medium move more easily, and hence that the pulses become
oblique; a far less satisfactory and consistent hypothesis than that of
Huyghens, of which we shall next have to speak. But Hooke has the
merit of having also combined with his theory, though somewhat
obscurely, the Principle of Interferences, in the application which he
makes of it to the colors of thin plates. Thus 66 he supposes the light to be
reflected at the first surface of such plates; and he adds, “after two
refractions and one reflection (from the second surface) there is
propagated a kind of fainter ray,” which comes behind the other reflected
pulse; “so that hereby (the surfaces and being so near together that
the eye cannot discriminate them from one), this compound or duplicated
pulse does produce on the retina the sensation of a yellow.” The reason
for the production of this particular color, in the case of which he here
speaks, depends on his views concerning the kind of pulses appropriate
to each color; and, for the same reason, when the thickness is different,
he finds that the result will be a red or a green. This is a very remarkable
anticipation of the explanation ultimately given of these colors; and we
may observe that if Hooke could have measured the thickness of his thin
plates, he could hardly have avoided making considerable progress in the
doctrine of interferences.
62
Diopt. c. ii. 4.

63
Meteor. c. viii. 6.

64
Micrographia, p. 56.

65
Micrographia, p. 57.

66
Micrographia, p. 66.

But the person who is generally, and with justice, looked upon as the
great author of the undulatory theory, at the period now under notice, is
Huyghens, whose Traité de la Lumière, containing a developement of his
theory, was written in 1678, though not published till 1690. In this work
he maintained, as Hooke had done, that light consists in undulations, and
expands itself spherically, nearly in the same manner as sound does; and
he referred to the observations of Römer on Jupiter’s satellites, both to
prove that this difference takes place successively, and to show its
exceeding swiftness. In order to trace the effect of an undulation,
Huyghens considers that every point of a wave diffuses its motion in all
directions; and hence he draws the conclusion, so long looked upon as
the turning-point of the combat between the rival theories, that the light
will not be diffused beyond the rectilinear space, when it passes through
an aperture; “for,” says he, 67 “although the partial waves, produced by
the particles comprised in the aperture, do diffuse themselves beyond the
rectilinear space, these waves do not concur anywhere except in front of
the 87 aperture.” He rightly considers this observation as of the most
essential value. “This,” he says, “was not known by those who began to
consider the waves of light, among whom are Mr. Hooke in his
Micrography, and Father Pardies; who, in a treatise of which he showed
me a part, and which he did not live to finish, had undertaken to prove,
by these waves, the effects of reflection and refraction. But the principal
foundation, which consists in the remark I have just made, was wanting
in his demonstrations.”
67
Tracts on Optics, p. 209.

By the help of this view, Huyghens gave a perfectly satisfactory and

correct explanation of the laws of reflection and refraction; and he also
applied the same theory, as we have seen, to the double refraction of
Iceland spar with great sagacity and success. He conceived that in this
crystal, besides the spherical waves, there might be others of a spheroidal
form, the axis of the spheroid being symmetrically disposed with regard
to the faces of the rhombohedron, for to these faces the optical
phenomena are symmetrically related. He found 68 that the position of the
refracted ray, determined by such spheroidal undulations, would give an
oblique refraction, which would coincide in its laws with the refraction
observed in Iceland spar; and, as we have stated, this coincidence was
long after fully confirmed by other observers.
68
Tracts on Optics, 237.

Since Huyghens, at this early period, expounded the undulatory theory

with so much distinctness, and applied it with so much skill, it may be
asked why we do not hold him up as the great Author of the induction of
undulations of light;—the person who marks the epoch of the theory? To
this we reply, that though Huyghens discovered strong presumptions in
favor of the undulatory theory, it was not established till a later era, when
the fringes of shadows, rightly understood, made the waves visible, and
when the hypothesis which had been assumed to account for double
refraction, was found to contain also an explanation of polarization. It is
then that this theory of light assumes its commanding form; and the
persons who gave it this form, we must make the great names of our
narrative; without, however, denying the genius and merit of Huyghens,
who is, undoubtedly, the leading character in the prelude to the
discovery.

The undulatory theory, from this time to our own, was unfortunate in
its career. It was by no means destitute of defenders, but these were not
experimenters; and none of them thought of applying it to 88 Grimaldi’s
experiments on fringes, of which we have spoken a little while ago. And
the great authority of the period, Newton, adopted the opposite
hypothesis, that of emission, and gave it a currency among his followers
which kept down the sounder theory for above a century.

Newton’s first disposition appears to have been by no means averse to

the assumption of an ether as the vehicle of luminiferous undulations.
When Hooke brought against his prismatic analysis of light some
objections, founded on his own hypothetical notions, Newton, in his
reply, said, 69 “The hypothesis has a much greater affinity with his own
hypothesis than he seems to be aware of; the vibrations of the ether being
as useful and necessary in this as in his.” This was in 1672; and we might
produce, from Newton’s writing, passages of the same kind, of a much
later date. Indeed it would seem that, to the last, Newton considered the
assumption of an ether as highly probable, and its vibrations important
parts of the phenomena of light; but he also introduced into his system
the hypothesis of emission, and having followed this hypothesis into
mathematical detail, while he has left all that concerns the ether in the
form of queries and conjectures, the emission theory has naturally been
treated as the leading part of his optical doctrines.
69
Phil. Trans. vii. 5087.