blue sky history

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A Blue SkyHistory

Pedro Lilienfeld

One of the most pervasive of opti-cal phenomena is the str ikinglyblue color of the clear daytime

sky, a sight that, because of air pollutionand urban sprawl, is becoming increas-ingly difficult to appreciate.

Throughout recorded history,peoplehave taken note of the hues assumed bythe sky under different viewing condi-tions; the most learned among themhave sought to understand the physicalorigins of the colors that characteri ze it .In the ancient Greek Cyclades, sky bluewas considered a fortuitous shade thatcould keep evil away,a superstition that

32 Optics & Photonics News ■ June 2004

A Blue SkyHistory

Pedro Lilienfeld

1047-6938/04/ 06/0032/8-$0015.00 ©O ptical Society of America

darkness of the night with the light of thedust and haze particles in the air illumi-nated by the sun.”

If we choose to identi fy an individualas the father of skylight optics the distinc-tion should be accorded to Leonardo daVinci (1452–1519). The wri tings of thegenius of the Renaissance contain tanta-lizing insights into the originsof the sky’s blueness and the appearance of smokes and mists, including those gener-ated under experimentally controlledcondit ions.Da Vinci’s interest in suchphenomena sprung from his keen artisticeye: his motivation in studying the sky

continues to find expression in theform of blue church cupolas, blue tr imaround buildings and turquoise jewelry

and clothing.Aristotle’s elucubrationson the color of the sky were drafted24 centuries ago. They are of great his-torical interest but show that the greatthinker had li tt le understanding of theorigins of the sky’s hue.

Perhaps the earliest serious attempt toexplain the sky’s color was made by theArab savant Aby Yusuf Yaquib ibn Ishaqal-Sabbah Al-Kindi (c.800–873) wholived in what is now Iraq.He attributedthe azure of the sky to “a mixture of the


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June2004 ■ Optics & Photonics News 33

And i f the sky, as you see it, ends on a

low plain, that lowest porti on of the

sky will be seen through a denser and

whiter atmosphere, which wil l weaken its true color as seen through that

medium, and the sky wil l look whiter

than it i s above you, where the li ne of

sight t ravels through a smal ler space

of air charged wi th heavy vapor.

Da Vinci became aware that the skybecame darker as one ascended the Alps.He correctly attributed the phenomenonto the thinning of the air as a functionof alt itude, concluding that above the

Although ideas about the origins of

the sky’s blue color can be traced back to

Greek antiquity, the first concerted effort to

reach a plausible explanation is attributed to

Leonardo da Vinci. The Italian master was followedby Newton, and later by Bouguer and de Saussure. Tyndall

wrestled with the problem around 1869, but the definitive

explanation would be proposed only in 1899, by Lord Rayleigh.

was related to the problems of aerial per-spective he faced in landscape painting.The perspicacious mind of the great mas-

ter is evident in the following excerptsfrom his notebooks:

You know that i n an atmosphere

of equal density the remotest objects

seen through it , as mountains, in

consequence of the great quanti ty of

atmosphere between your eye and them

appear blue and almost of the same hue

as the atmosphere itself when the sun is

in the East. Hence you must make the

nearest bui lding above the wall of its

real color, but make the more distant

ones less defined and bluer; thus, if one

is to be five times as distant , make it

five times bluer. And by this rule the buildi ngs which above a [given] li ne

appear of the same size wi ll plainly

be disti nguished as to which are the

most remote and which are larger

than the others.

Another of da Vinci’s wri tingsgives voice to an early interpretationof atmospheric turbidity as manifestedby the whitening of the sky near thehorizon:


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atmosphere the sky must appear black.His interpretation of the origin of thesky’s blue color, however, proved to beonly part ially correct. He wrote:

I say that the blue which is seen in the

atmosphere is not i ts own color, but i s caused by the heated moisture having

evaporated into the most minute

imperceptible part icles, which the

beams of the solar rays att ract and

cause to seem luminous against the

deep intense darkness of the region …

above them. And this may be seen, as

I myself saw it , by anyone who ascends

Mon Boso,* a peak of the Alps that

divides France from It aly … And I saw

the atmosphere dark overhead, and the

rays of the sun str iki ng the mountain

had far more brightness than i n the plains below, because less thi ckness of

atmosphere lay between the summi t

of this mountain and the sun.

The preceding paragraph is trulystr iking in its insights,except of coursefor the idea that minute water dropletsdispersed through the atmosphere con-stitute the scattering medium that yieldsthe sky’s blue color, a misconception thatwould persist for another 400 years,untilthe very end of the 19th century.

Isaac Newton (1642–1727) was unableto provide a better explanation for thesky’s blue color than that provided byda Vinci almost two centuries earl ier.Sti ll ,the great English mathematician had a farmore thorough understanding of opticalphenomena. He suggested an earlyawareness of the spectral dependence of light scattering on particle size in whatcame to be known,two-and-a-half cen-turies later, as the Rayleigh regime:

The blue of the fi rst Order, though very

faint and li tt le,may possibly be the

Colour of some Substances; and par ti c- ularly the azure Colour of the Skies

seems to be of this Order. For al l

Vapours when they begin to condense

and coalesce into smal l Parcels, become

fi rst of that Bigness, whereby such an

Azure must be reflected before they can

consti tute Clouds of other Colours.And

so thi s being the fir st Colour whi ch

Vapours begin to reflect, it ought to be

the Colour of the finest and most trans- parent Skies, in which Vapours are not

arrived to that Grossness requisite to

reflect other Colours, as we find it is

by Experience.

The Age of Enligh tenm ent

The expansion of the sciences in the 17th

century set the stage for them to takehold on a much broader scale in the 18th

century.As experimentation unbur-dened by medieval preconceptions beganto prevail , methodologies became more

rigorous and even quantitative. In thefield of atmospheric visibil ity and lighttransmission in the 1700s, two scientistsstand out: Bouguer and de Saussure.

Pierre Bouguer (1698–1758) is knownprincipally for the exponential attenua-tion law for light traversing a homoge-neous medium, also known as theBouguer-Lambert-Beer law (Bouguerpredated both Lambert and Beer).Thiscontribution secures Bouguer’s place asa founding father of atmospheric optics.The great scientist was a child prodigy,

having succeeded—at the age of 15—hisfather as Royal Professor of Hydrographyupon the latter’s death in 1713.

November 23,1725,can be consideredthe birthday of atmospheric photometry.It was on that day, in Brittany, thatBouguer first quantified the light attenua-tion of Earth’s atmosphere.The methodhe used was ingenious,constrained as hewas by having as his only light sensor thehuman eye. Bouguer assumed that, if heused the moon as the source of illumina-

tion, Earth’s atmosphere could be consid-ered a thin plate.He further surmised(correctly) that if he could measure theatmospheric brightness of moonlight attwo different angles,he could determine

the atmospheric transmission. Bouguerused the light of a candle as a reference tocompare the brightness of the moon atthe two angles.Remarkably,he circum-vented the nonlineari ty of the humaneye’s irradiance response by varying thedistance to the candle and using Kepler’sinverse square law to quanti fy thechanges in brightness.Bouguer was thusable to determine that the pre-IndustrialRevolution air in Brittany was indeed,byour standards,of pristine purity.

Bouguer’s method exemplifies thegeneral approach to measurement used

over several centuries before the availabil-ity of sensors and detectors.This methodconsisted of using one of the humansenses as a relative measurement device,i.e., comparing the perceived magnitudeof the sensory stimulus against areference. Bouguer went on to make sig-nif icant contr ibutions to other areas of science and technology. He distinguishedhimself as the principal participant inan eight-year-long scientific mission,sponsored by the Académie Royale desSciences, to what is now Ecuador, to

determine the spheroidal shape of Earth.Horace-Bénédict de Saussure was

born near Geneva, Switzerland, in 1740.He attended the Académie de Genève,where at the age of 19 he produced histhesis “Dissertation on the Nature of Fire”(Di ssertat io physica de igne ). At the age of 22,he became a professor of physics andphilosophy.Perhaps history’s first scien-ti fi c mountaineer, de Saussure wasresponsible for the first ascent to the sum-mit of Mont Blanc in the Alps,where hecarried out barometric pressure and

atmospheric transparency measurements.De Saussure wrote two papers whichwere published in 1789, the year of theFrench Revolution, that have seminal rel-evance to the field of atmospheric pho-tometry.The first describes a cyanometer,an apparatus used to quantify the degreeof blueness of the sky. It consists of anannulus with 53 radial sectors,each of which has a slightly different depth of blueness.The colors progress from purewhite (the absence of blue) to deep,


ATMOSPHERIC OPTICS

* Believed to be Monte Rosa.

I saw the atmosphere

dark overhead, and the

rays of the sun striking

the m ountain had farmo re b rightness than

in the p lains be low,

because less thickness of

atmosphere lay between

the summ it of this

mountain and the sun.

—Leonardo da Vinci


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De Saussure wrote two

pap ers which were published

in 1789. The first d escribes

a cyanom eter, an app aratusused to q uantify the d eg ree

of b lueness o f the sky. It

consists of an annulus with

53 radial secto rs, each

of which has a slig htly

different dep th

of blueness.


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Prussian blue,on to mixtures of intense

blue and gradually increasing amounts of India ink black. This range of color gra-dations was intended to simulate thegamut from a milky (perhaps polluted)sky to the appearance of the sky abovethe atmosphere.The steps of increasingblueness were based on a visual thresholddetermination normalized against a visi-bility contrast referenced against a black-on-white target. De Saussure definedthese minimum color discriminationsteps as “nuances.” He reported simulta-neous “measurements” (by visual match-

ing of the sky’s blueness with one of thewheel’s sectors) at three different sites:Geneva, Chamonix and on the slope of Mont Blanc at an alti tude of 3,436 meters.Both zenith and horizontal observationswere tabulated.The data of the zenithmeasurements clearly indicated thedeeper blueness of the sky as seen fromthe elevated Mont Blanc site.Remarkably,de Saussure interpreted his results asproof that “the color of the sky deter-mined by the cyanometer is the measureof the quantity of concrete vapors in sus-

pension in the air,” defining such “con-crete vapors” (i .e.,particles in suspension)by contrasting them with “vapors that aredissolved” in the air ( i.e., in the gas phase,in modern terminology).

The 19 th century

Dominique François Arago (1786–1853)made major contributions to variousbranches of physics, including postula-tion of the definit ive test to decidebetween the corpuscular and the

undulatory theories of light. (The test,

ultimately performed by Foucault in1850, confirmed the wave nature of light. Today’s accepted wave-part icleduality concept was derived by means of de Broglie’s quantum mechanical analysisin the 1920s.) A significant advance of theearly 19th century was Arago’s discovery,in 1809, of the polarization of daytimeskylight at 90 degrees to the directionof the sun.

Yet Arago’s observations introducedan element of confusion into the inter-pretation of the optical processunderly-

ing the skylight phenomenon. Rudolf Clausius (1822–1888), noted for his con-tr ibutions to thermodynamics, pointedout that refraction within macroscopicdroplets could not explain the color of the sky; he postulated the presence inthe atmosphere of minute water bubbles,an explanation inconsistent withArago’s observation. Sir John Herschel(1792–1871), son of the famousastronomer Wil liam Herschel, struggledwith the observed 90-degree polarizationin these terms:

The cause of the polarization is evi-

dently a reflecti on of the sun’s li ght

upon something.The questi on is, On

what? Were the angle of maximum

polar izati on 76°, we should look to

water or ice as the reflecti ng body, how-

ever inconceivable the existence in a

cloudless atmosphere on a hot summer’s

day of unevaporated molecules (part i-

cles?) of water. But though we were once

of thi s opinion, careful observati on has

satisfi ed us that 90°, or thereabouts, is a

correct angle, and that therefore,what- ever be the body on whi ch the light has

been reflected, if polar ized by a single

reflecti on, the polar izing angle must be

45°, and the index of refraction, which

is the tangent of that angle, unit y; in

other words, the reflecti on would

require to be made in air upon air!

Complete elucidation of the vexingpolarization effect could not be achievedby means of the macroscopic optics of refraction and reflection as understood

during the first half of the 19th century:it had to await Lord Rayleigh’s molecularscattering theory of 1871.

James David Forbes (d.1868),princi-pal of the University of St. Andrews andinventor of the seismometer,made theobservation that the sun appeared redwhen viewed through a section of thesteam plume of a locomotive.When herepeated the experiment in the laboratoryusing a small steam boiler, he found thatwhite light shining through the just-condensing detached part of the visible

steam plume underwent a similar red-dening.He concluded that this observa-tion recreated the optical processunderlying crimson sunsets,where theblue components have been preferentiallyscattered out of the primary beam.

An outstanding contributor to theunderstanding of atmospheric light scat-tering was John Tyndall (1820–1893),who is also remembered for his remark-able work in other fields.AmongTyndall’s many achievements are some


ATMOSPHERIC OPTICS

Pierre Bouguer.Sir Isaac Newton.(From a 1725 portrait by John Vanderban.)

A page from Leonardoda Vinci’sCodex

Leicester manuscript.

1480–1519

Leonardoda Vinci’smanuscripts.

1704

IsaacNewton’sOpticks .

1725

Bouguermeasuresatmospheric

transmission.

1400s 1700s

Milestones

in the under-

standing of

the origin

of the blue

color of the

da ytime sky.


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that are of major relevance to 21st centuryscience. They include the invention of thelight pipe,which led to the developmentof fiber optics, and pioneering work onthe trapping of infrared radiation by var-ious atmospheric gases, in other words,the “greenhouse” effect. Tyndall visitedthe Swiss Alps many times. It is worthnothing that, like da Vinci and deSaussure,Tyndall was stimulated by thesealpine excursions to investigate atmo-spheric optical phenomena.He pursuedthis interest in the context of his workon part icle light scattering,in particular

the examination of small part icles insuspension.

His most notable contr ibutions arethe first detailed observations of scatter-ing phenomena by particles smaller thanthe wavelength of the incident light, aswell as those the size of which approachesthat wavelength. He is also known for thefirst determination of the dependence of scattering irradiance on particle size (theTyndall effect) in what was later to becalled the Rayleigh regime.The fi rst sys-tematic observations of the effects of

particle size on the color and angle of scattered white light are also creditedto Tyndall.

Yet Tyndall was unable to resolve thepersistent question with which his prede-cessors and contemporaries had grappledwithout success: the true nature of thescattering medium that gives the sky itsblue color. Influenced by Leonardo daVinci and Newton, he continued toattribute the phenomenon to scatteringby minute water droplets in the high

atmosphere.Based on laboratory experi-

ments he concluded in 1869 that:

When the air was so sifted as to ent irely

remove the visible floati ng matter, it no

longer exerted any sensible action upon

the light, but behaved l ike a vacuum.

This sentence suggests that he did notrealize the integrating effect of a long—on the order of kilometers—paththrough a purely molecular atmospherewhich is required to yield a visibly bluescatter.As late as 1869, in reference to

the color and polarization of skylight,Tyndall had to admit “these questionsconstitute,in the opinion of our mosteminent authorities, the two great stand-ing enigmas of meteorology.”

The solution would in fact have toawait Rayleigh’s rigorous mathematicaltreatment and its subsequent interpreta-tion. Tyndall ’s unsuccessful search for thesource of the blue color of the daytimesky can be attributed to his reliance onelegant, heuristic conjecture as a meansto explain natural phenomena rather

than on rigorous mathematical analysis.Nevertheless, credit is due to Tyndall inthat his detailed and insightful experi-ments and observations provided thefoundation for the next generation of scientists to achieve the necessary break-throughs by applying the heretoforeinsufficient methodological rigor.

The solution to the enigma

The next breakthrough required themathematical solution of the scattering

of light by particles with dimensions

smaller than and comparable to theincident wavelength. A discussionregarding the primacy of attribution of these solutions would immerse us in averi table minefield. It involves a cast of well known and lesser known scientistsworking during the second half of the19th and the first half of the 20th century:Clebsch,Lorenz,Maxwell, Rayleigh, Mie,Debye and others.The debate over whowas the first to develop workable theorieson the scattering of light by small spheresis beyond the scope of this article.

The contributions of LudwigValentine Lorenz (1829–1891) havereceived due recognition since the 1980s.His name is cited with that of GustavMie in connection with the generalizedtheory of electromagnetic scattering (i .e.,Lorenz-Mie scattering). He is best knownto today’s physicists for the Lorentz-Lorenz equation that relates the refractiveindex to the dielectric constant of amedium. (Hendrick Lorentz developedthe equation independently,nearly con-currently, in 1870).

Lorenz’s principal contribution to thestudy of the optics of aerosols is found inan 1890 memoir in which he solves theproblem of the scattering of light by adielectri c sphere.For molecular sizedspheres, he derived the inverse fourthpower wavelength relationship thatagreed with the derivation made byRayleigh in 1871.Lorenz’s contributions,however, were largely ignored,presum-ably because he chose to publish hismemoir in his native language, Danish.

ATMOSPHERIC OPTICS

1809

Arago discovers sky-light polarization.

1871

Lord Rayleigh’sscatter theory.

1899

Lord Rayleigh’sdefinitive explanation

of the blue sky.

Issue of theMémoires de

Académie Royale de Turin that

ontains de Saussure’s papers

on atmospheric photometry.

Lord Rayleigh. John Tyndall.

1789

De Saussure’spapers onatmospheric

transmissionand bluenessof the sky.

1869

Tyndall andHerschel fail toexplain the blue sky.

1890

Lorenz’sscatter theory.

1913

Cabbanes’laboratory airscatter experiment.

1800s 1890-1900s


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He showed little interest in communicat-ing his results to physicists in other coun-tries and chose not to base his work onMaxwell’s recently developed electromag-netic propagation theory. Another of

Lorenz’s idiosyncrasies was his phe-nomenological view of physics; he soughtto keep ontological hypotheses and phys-ical assumptions out of physical theory.This may account for the fact thatLorenz,unlike Rayleigh,does not seemto have related his mathematical conclu-sions about light scattering by very smallparticles to real atmospheric phenomenasuch as the blue color of the sky.

We have now arrived at one of themost remarkable players in the field of light scattering,John Will iam Strutt ,Third Baron Rayleigh (1842–1919). The

span of Lord Rayleigh’s scientific workwas exceedingly wide.Considered bysome to be the last of the great Victorianpolymaths, his research ranged overnearly the enti re field of physics of thelate 19th century: sound, wave theory,color vision, electrodynamics, electro-magnetism, light scattering, fluid flow,hydrodynamics, density of gases, viscos-ity, capil larity,elasticity,photography andelectrical standards (ohm, ampere, volt).Among the many honors he received wasthe 1904 Nobel Prize in Physics for his

contribution to the discovery and isola-tion of argon. In 1905 he was electedpresident of the Royal Society.Rayleighwrote some 450 papers and retained hismental powers unti l the end, working onscienti fic writings unti l his death in 1919.

In 1871,Rayleigh published his fi rstpaper on the subject that concerns us:“On the light from the sky, its polariza-tion and colour,” followed immediatelyby another entitled: “On the scattering of light by small particles.” This early workwas based on elastic-wave equations

where,as expected for that period, etheris the oscillating medium. This was a nat-ural extension of Rayleigh’s interest in thebehavior of sound.In the first of thesepapers,Rayleigh develops for the fi rsttime his now famous equation:

92 ε–1 2 nV 2I / I 0= —– —— (1+cos2)——2 ε+2 4r 2

where I 0 and I are the incident (unpolar-ized) and scattered irradiances, ε is the

dielectric permi ttivity of the part iclerelative to the surrounding medium, isthe scattering angle, n is the number of scattering particles,V is the particle vol-ume, is the wavelength of the incidentlight, and r is the distance between thescattering particles and the observer (ordetector). This equation explains theenti re scattering behavior of part icles

the size of which is negligible withrespect to the wavelength: the strongsize dependence (the sixth power of diameter) , the angular symmetry andpolarization and, most importantly, theinverse fourth power dependence onwavelength. As we shall see, the latterwas to lead Rayleigh, 18 years later, tothe definit ive explanation of the bluecolor of the sky.

A decade later, Rayleigh had incorpo-rated Maxwell ’s electromagnetic theory

of light into his own wri tings. In 1899he published perhaps his most famouspaper, which settled the puzzle once andfor all. It appears from Rayleigh’s ownassertion that he may have been led to theorigin of the sky’s blue color as a result of a letter that he received from Maxwell in1873 which, in turn, had been inspired byRayleigh’s 1871 paper. It is worth citing

Rayleigh’s introductory remarks to his1899 paper:

This subject has been treated in papers

published many years ago. I resume it

in order to examine more closely than

hitherto the attenuati on undergone by

the primary li ght on i ts passage through

a medium containing small part icles, as

dependent upon the number and size

of the part icles. Closely connected wi th

this is the interesti ng questi on whether


ATMOSPHERIC OPTICS


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the li ght from the sky can be explained

by diffracti on* from the molecules of air

themselves, or whether i t i s necessary to

appeal to suspended particles composed

of foreign matter, solid or li quid. It will

appear, I think, that even in the absence

of foreign parti cles we should sti ll have

a blue sky.

The latter was a remarkably cautiousstatement about the definitive solution tothe centuries old enigma. It is worthy of note that today we have come to the com-plementary realization that the presenceof such “particles … of foreign matter”actually degrades the blueness of the sky.

Finally,Rayleigh reaches an impor-tant, insightful quali tative conclusion,

fully supported by modern theoreticalanalysis:

If the view, suggested in the present

paper, that a large part of the li ght

diffracted from the molecules them-

selves, be correct, the observed incom-

plete polar izati on at 90°from the Sun

may be part ly due to the molecules

behaving rather as elongated bodies with indifferent orientation than as

spheres of homogeneous material.

It is of interest that, as late as 1908,Rayleigh’s definit ive identification of themedium that causes the sky’s bluenesswas sti ll being questioned,and alternativeexplanations such as ozone fluorescencewere sti ll being postulated.

The actual experimental confirmationthat air molecules do scatter light was

apparently achieved for the first time byJean Cabannes (1885–1959) in 1913.

Postscript

Why is the clear daytime sky blue and not

violet, since violet has an even shorterwavelength?The blue color is the result of the combined effects of the incoming solarir radiance spectrum, the inverse four thpower scattering dependence and thephotopic response of the human eye.Asda Vinci postulated centuries ago, the blueappearance requires the dark backgroundof empty space beyond the atmosphere.Thus,the irradiance from a backgroundof sun-li t clouds overwhelms that causedby the blue molecular scattering.

Since the blue of the sky is not anintrinsic color of air, the color of anyplanetary atmosphere viewed against theblack of space and i lluminated by a sun-like star will also be blue,on condit ionthat Lorenz-Mie scattering and wave-length-selective absorption processes donot predominate, as in the case of Marswith its thin atmosphere and reddishsuspended dust, or Venus with its thicksulfuric acid aerosol cloud cover.

Most surprisingly,more than a cen-tury after Rayleigh published his solu-tion,present day understanding of theorigin of the sky’s blueness remains

imperfectly disseminated.Respectedsources, such as the EncyclopediaBritannica, sti ll misattribute the causeof this phenomenon.

Pedro Lilienfeld (pe dro.lilienfeld@therm o.com )

is principal science ad visor at The rmo Electron

Corporation, Franklin, M ass. He sp ecializes in

aerosol physics and instrumentation.

Further reading

1. J. D. Hey, From Leonardo to the Graser: LightScattering in Historical Perspective (Part I), SouthAfrican J. of Sci. 79:11-27 (1983).

2. L. da Vinci, (1508), The Notebooks, E. MacCurdy, ed.,Konecky & Konecky 2003.

3. N.A. Logan, Survey of Some Early Studies of the

Scattering of Plane Waves by a Sphere, Proc. IEEE53:773-85 (1965).

4. Sir Isaac Newton, Opticks, or a Treatise of theReflections, Refractions, Inflections & Colours of Light,Book Two, Part III, Prop. VII, 255-62 (1730).

5. Lord Rayleigh, On the Transmission of Light Throughan Atmosphere Containing Small Particles inSuspension, and on the Origin of the Blue of the Sky,Phil. Mag. Ser. 5, 47:375-84 J. W. Strutt, (1899).

6. A. T. Young, Rayleigh Scattering, Physics Today 35 (1)42-8 (1982).

7. J. P. Richter, The Notebooks of Leonardo da Vinci, 1,Dover Publications (1970).

8. Applied Optics 3 (10) is a special issue dedicatedentirely to Lord Rayleigh.

9. C. F. Bohren, “Atmospheric Optics,” in The OpticsEncyclopedia, 53-91, Th. G. Brown et al., eds., Wiley-VCH, 2004.

ATMOSPHERIC OPTICS

* Rayleigh’s “diffraction” in this context is most proba-

bly equivalent to our concept of scattering.

This mo untain range in

British Columb ia, far from

urban sp rawl and sources of air

po llution, affords an o pp ortu-

nity to app reciate the brilliant

blue color of the daytime sky.

blue sky history

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