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Chapter 35

The Nature of Light and the

Laws of Geometric Optics

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The Nature of LightBefore the beginning of the nineteenthcentury, light was considered to be a stream

of particlesThe particles were either emitted by theobject being viewed or emanated from theeyes of the viewer

Newton was the chief architect of the particletheory of lightHe believed the particles left the object andstimulated the sense of sight upon entering theeyes

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Nature of Light

Alternative ViewChristian Huygens argued that lightmight be some sort of a wave motion

Thomas Young (1801) provided the firstclear demonstration of the wave natureof light

He showed that light rays interfere witheach other Such behavior could not be explained byparticles

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More Confirmation of Wave

NatureDuring the nineteenth century, other developments led to the generalacceptance of the wave theory of lightMaxwell asserted that light was a formof high-frequency electromagnetic waveHertz confirmed Maxwells predictions

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Particle NatureSome experiments could not beexplained by the wave nature of light

The photoelectric effect was a major phenomenon not explained by waves

When light strikes a metal surface,electrons are sometimes ejected from thesurfaceThe kinetic energy of the ejected electronis independent of the frequency of the light

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Particle Nature, cont.Einstein (in 1905) proposed anexplanation of the photoelectric effectthat used the idea of quantization

The quantization model assumes that theenergy of a light wave is present in

particles called photonsE = h

h is Plancks Constant and = 6.63 x 10 -34 J .s

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Dual Nature of LightIn view of these developments, lightmust be regarded as having a dual

natureLight exhibits the characteristics of awave in some situations and thecharacteristics of a particle in other situations

Nature prevents testing both qualities atthe same time

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Measurements of the

Speed of LightSince light travels at a very high speed,early attempts to measure its speedwere unsuccessful

Remember c = 3.00 x 10 8 m/s

Galileo tried by using two observersseparated by about 10 km

The reaction time of the observers wasmore than the transit time of the light

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Measurement of the Speed of

Light Roemers MethodOle Roemer (1675)used astronomical

observations toestimate the speedof lightHe used the periodof revolution of Io, amoon of Jupiter, asJupiter revolvedaround the sun

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Roemers Method, cont.The periods of revolution were longer when the Earth was receding from Jupiter

and shorter when the Earth was approachingUsing Roemers data, Huygens estimatedthe lower limit of the speed of light to be

2.3 x 108

m/sThis was important because it demonstratedthat light has a finite speed as well as givingan estimate of that speed

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Measurements of the Speed

of Light Fizeaus MethodThis was the first successful method for measuring the speed of light by means

of a purely terrestrial techniqueIt was developed in 1849 by ArmandFizeau

He used a rotating toothed wheelThe distance between the wheel(considered to be the source) and amirror was known

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Fizeaus Method, cont.d is the distancebetween the wheeland the mirror t is the time for one

round tripThen c = 2 d / t

Fizeau found avalue of c = 3.1 x 10 8 m/s

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The Ray Approximation in

Geometric OpticsGeometric optics involves the study of thepropagation of light

It uses the assumption that light travels in astraight-line path in a uniform medium andchanges its direction when it meets thesurface of a different medium or if the opticalproperties of the medium are nonuniform

The ray approximation is used to represent

beams of light

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Ray ApproximationThe rays are straightlines perpendicular to the wave frontsWith the rayapproximation, weassume that a wave

moving through amedium travels in astraight line in thedirection of its rays

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Ray Approximation, cont.If a wave meets abarrier, we will

assume that

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Reflection of LightA ray of light, the incident ray , travels ina mediumWhen it encounters a boundary with asecond medium, part of the incident rayis reflected back into the first medium

This means it is directed backward into thefirst medium

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Specular

ReflectionSpecular reflection is reflection from a

smooth surfaceThe reflected raysare parallel to eachother All reflection in thistext is assumed tobe specular

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Diffuse

ReflectionDiffuse reflection isreflection from a roughsurfaceThe reflected rays travelin a variety of directionsA surface behaves as asmooth surface as longas the surfacevariations are muchsmaller than thewavelength of the light

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Law of ReflectionThe normal is a lineperpendicular to thesurface

It is at the point wherethe incident ray strikesthe surface

The incident ray makesan angle of 1 with the

normalThe reflected ray makesan angle of 1 with thenormal

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Active Figure 35.6

(SLIDESHOW MODE ONLY)

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Law of Reflection, cont.The angle of reflection is equal to theangle of incidence 1= 1

This relationship is called the Law of Reflection

The incident ray, the reflected ray andthe normal are all in the same plane

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Multiple ReflectionsThe incident ray strikes thefirst mirror The reflected ray is directedtoward the second mirror There is a second reflectionfrom the second mirror Apply the Law of Reflectionand some geometry todetermine information aboutthe rays

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RetroreflectionAssume the angle between two mirrorsis 90 o

The reflected beam returns to thesource parallel to its original pathThis phenomenon is calledretroreflection

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Refraction of LightWhen a ray of light traveling through atransparent medium encounters a boundary

leading into another transparent medium, partof the energy is reflected and part enters thesecond mediumThe ray that enters the second medium isbent at the boundary

This bending of the ray is called refraction

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Refraction, 2The incident ray, the reflected ray, therefracted ray, and the normal all lie on the

same planeThe angle of refraction depends upon thematerial and the angle of incidence

v 1 is the speed of the light in the first medium andv 2 is its speed in the second

2 2

1 1

sinconstantsin

v

v

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Refraction of Light, 3The path of the lightthrough the refracting

surface is reversibleFor example, a ray thattravels from A to B

If the ray originated atB, it would follow theline AB to reach pointA

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Following the Reflected and

Refracted RaysRay is the incident rayRay is the reflected

rayRay is refracted intothe luciteRay is internally

reflected in the luciteRay is refracted as itenters the air from thelucite

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Active Figure 35.10

(SLIDESHOW MODE ONLY)

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Refraction Details, 1Light may refractinto a materialwhere its speed islower The angle of refraction is lessthan the angle of incidence

The ray bendstoward the normal

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Refraction Details, 2Light may refractinto a materialwhere its speed ishigher The angle of refraction is greater than the angle of incidence

The ray bends away from the normal

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Light in a MediumThe light enters from the leftThe light may encounter an

electronThe electron may absorb thelight, oscillate, and reradiatethe light

The absorption and radiationcause the average speed of the light moving through thematerial to decrease

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Active Figure 35.11

(SLIDESHOW MODE ONLY)

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The Index of RefractionThe speed of light in any material is lessthan its speed in vacuumThe index of refraction , n, of amedium can be defined as

speed of light in a vacuum c

n speed of light in a medium v

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Index of Refraction, cont.For a vacuum, n = 1

We assume n = 1 for air also

For other media, n > 1n is a dimensionless number greater than unity

n is not necessarily an integer

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Some Indices of Refraction

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Frequency Between MediaAs light travels fromone medium toanother, its frequency does not change

Both the wave speedand the wavelength dochange

The wavefronts do notpile up, nor are createdor destroyed at theboundary, so muststay the same

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Index of Refraction ExtendedThe frequency stays the same as the wavetravels from one medium to the other

v = 1 = 2 but v 1 v 2 so 1 2

The ratio of the indices of refraction of the twomedia can be expressed as various ratios

1 1 21

2 2 12

c v nn

c v nn

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More About Index of

RefractionThe previous relationship can besimplified to compare wavelengths and

indices: 1n 1 = 2n 2In air, n 1 1 and the index of refractionof the material can be defined in termsof the wavelengths

in vacuumin a mediumn

n

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Snells Law of Refractionn 1 sin 1 = n 2 sin 2

1 is the angle of incidence

2 is the angle of refraction

The experimental discovery of thisrelationship is usually credited toWillebrord Snell and is therefore knownas Snells law of refraction

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Snells Law ExampleLight is refracted intoa crown glass slab 1 = 30.0 o, 2 = ?n 1 = 1.00 and n2 =1.52

From Table 35.1

2

= sin -1(n1

/ n2) sin

1

= 19.2 o

The ray bends towardthe normal, asexpected

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Huygenss PrincipleHuygens assumed that light is a form of wave motion rather than a stream of

particlesHuygenss Principle is a geometricconstruction for determining the position

of a new wave at some point based onthe knowledge of the wave front thatpreceded it

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Huygenss Principle, cont.All points on a given wave front aretaken as point sources for the

production of spherical secondarywaves, called wavelets, whichpropagate outward through a mediumwith speeds characteristic of waves in

that mediumAfter some time has passed, the newposition of the wave front is the surface

tangent to the wavelets

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Huygenss Construction for a

Plane WaveAt t = 0, the wave front isindicated by the plane AAThe points arerepresentative sources for the waveletsAfter the wavelets havemoved a distance c t , anew plane BB can bedrawn tangent to thewavefronts

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Huygenss Construction for a

Spherical WaveThe inner arcrepresents part of thespherical waveThe points arerepresentative pointswhere wavelets arepropagated

The new wavefront istangent at each point tothe wavelet

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Huygenss Principle and the

Law of ReflectionThe law of reflection canbe derived fromHuygenss principle

AB is a wave front of incident light

The wave at A sends outa wavelet centered on A

toward DThe wave at B sends outa wavelet centered on B toward C

AD = BC = c t

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Huygenss Principle and the

Law of Reflection, cont.Triangle ABC iscongruent to triangle

ADC cos = BC / AC cos = AD / AC Therefore, cos = cos and = This gives 1 = 1

This is the law of reflection

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Huygenss Principle and the

Law of RefractionRay 1 strikes thesurface and at atime interval t later,ray 2 strikes thesurfaceDuring this timeinterval, the wave at

A sends out awavelet, centered at

A , toward D

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Huygenss Principle and the

Law of Refraction, cont.The wave at B sends out a wavelet,centered at B, toward C

The two wavelets travel in differentmedia, therefore their radii are differentFrom triangles ABC and ADC , we find

1 21 2sin and sin

BC v t AD v t

AC AC AC AC

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Huygenss Principle and the

Law of Refraction, finalThe preceding equation can be simplifiedto

This is Snells law of refraction

1 1

2 2

1 1 2

2 2 1

1 1 2 2

sinsin

sinBut

sin

and so sin sin

v

v

c n n

c n n

n n

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DispersionFor a given material, the index of refraction varies with the wavelength of

the light passing through the materialThis dependence of n on is calleddispersionSnells law indicates light of differentwavelengths is bent at different angleswhen incident on a refracting material

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Variation of Index of

Refraction with WavelengthThe index of refractionfor a material generally

decreases withincreasing wavelengthViolet light bends morethan red light whenpassing into a refractingmaterial

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Angle of DeviationThe ray emergesrefracted from its

original direction of travel by an angle ,called the angle of deviation

The angle of deviation dependson the wavelength

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Refraction in a PrismSince all the colorshave differentangles of deviation,white light willspread out into aspectrum

Violet deviates themostRed deviates the leastThe remaining colorsare in between

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The RainbowA ray of light strikes a drop of water inthe atmosphere

It undergoes both reflection andrefraction

First refraction at the front of the drop

Violet light will deviate the mostRed light will deviate the least

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The Rainbow, 2At the back surface the lightis reflectedIt is refracted again as itreturns to the front surfaceand moves into the air The rays leave the drop atvarious angles

The angle between the whitelight and the most intenseviolet ray is 40The angle between the whitelight and the most intense redray is 42

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Active Figure 35.23

(SLIDESHOW MODE ONLY)

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Observing the Rainbow

If a raindrop high in the sky is observed, the red ray is

seenA drop lower in the sky would direct violet light to theobserver The other colors of the spectra lie in between the redand the violet

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Double RainbowThe secondary rainbowis fainter than theprimary

The secondary rainbowarises from light thatmakes two reflectionsfrom the interior surfacebefore exiting theraindropHigher-order rainbowsare possible, but their intensity is low

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Total Internal Reflection

A phenomenon called total internalreflection can occur when light is

directed from a medium having a givenindex of refraction toward one having alower index of refraction

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Critical Angle

There is a particular angle of incidence thatwill result in an angle of refraction of 90

This angle of incidenceis called the critical angle, C

21 2

1

sin (for )C n

n nn

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Active Figure 35.26

(SLIDESHOW MODE ONLY)

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Critical Angle, cont.For angles of incidence greater than thecritical angle, the beam is entirely

reflected at the boundaryThis ray obeys the law of reflection at theboundary

Total internal reflection occurs onlywhen light is directed from a medium of a given index of refraction toward amedium of lower index of refraction

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Fiber OpticsAn application of internalreflectionPlastic or glass rods are

used to pipe light fromone place to another Applications include:

medical use of fiber optic cables for diagnosis and correctionof medical problemsTelecommunications

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Fiber Optics, cont.A flexible light pipeis called an optical

fiber A bundle of parallelfibers (shown) canbe used to construct

an opticaltransmission line

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Construction of an OpticalFiber

The transparentcore is surrounded

by cladding The cladding has a lower n than the coreThis allows the light inthe core to experience

total internal reflectionThe combination issurrounded by the

jacket

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Fermats Principle

Pierre de Fermat developed a generalprinciple that can be used to determine

the path that light follows as it travelsfrom one point to another Fermats principle states that when a

light ray travels between any twopoints, its path is the one thatrequires the smallest time interval

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Fermats Principle, SomeConsequences

The paths of light in a homogenousmedium are straight lines

Because a straight line is the shortestdistance between two points

With the help of some geometry,

Fermats principle can be used to deriveSnells law of refraction and the law of reflection