Chapter 33Chapter 33 - erbion.com 33.pdf · – X-ray optics – Y-rays PHYS52 Eradat SJSU 3. What is light? It' bi d it' l ! N ! It' S !It's a bird, no, it's a plane ! No ! It's

Chapter 33Chapter 33

• 33 1 The Nature of light & its propagation33.1 The Nature of light & its propagation• 33.2 The laws of reflection & refraction,

Index of refractionIndex of refraction• 33.3 Total internal reflection (TIR)• 33.4 Dispersion• 33.5 Polarization• 33.6 Scattering of light• 33 7 Huygens’principle• 33.7 Huygens principle

1PHYS52 Eradat SJSU

OpticsOptics

• Optics is a branch of physics that deals withOptics is a branch of physics that deals with – Propagation of light– Interaction of light with matterInteraction of light with matter – Light’s behavior at interfaces of different

mediamedia• Photonics is a branch of physics that deals with

– Production of light– Production of light– Absorption of light

2PHYS52 Eradat SJSU

Sub-branches of opticsSub branches of optics• Linear optic

– Imaging OpticsImaging Optics– Non-imaging optics

• Nonlinear opticso ea opt cs• Optics of different frequency ranges of the

Electromagnetic Spectra i.e. – visible optics (or simply optics) – Radio frequency optics– Infrared optics– X-ray optics– Y-rays

3PHYS52 Eradat SJSU

What is light?It' bi d it' l ! N ! It' S !It's a bird, no, it's a plane ! No ! It's Superman !

• 1642-1727 Stream of particles called corpuscles (Newotonian)p p ( )• 1803 Idea of light being a wave grew strong Young’s work.• 1873 Maxwell established (theoretically) that light is an

electromagnetic waveelectromagnetic wave • 1887 Hertz showed experimentally that light is indeed composed

of electromagnetic waves. • 1900 Max Planck showed that the electromagnetic radiation is

emitted in quanta (packets) of energy. He named them photons. • 1905 Following Planck’s work Einstein in 1905 was able to1905 Following Planck s work Einstein in 1905 was able to

explain the photoelectric effect. • 1930 By birth of quantum electrodynamics the two pictures are

“kind of” reconciled but the debate is still going onkind of reconciled but the debate is still going on. 4PHYS52 Eradat SJSU

What is light?What is light?

• Light has a dual natureLight has a dual nature. – At times it behaves like an electromagnetic

wavewave – At times it behaves like a particle or quantum

of energy.of energy. • It is up to us to recognize which model is

appropriate for a particular situationappropriate for a particular situation.

5PHYS52 Eradat SJSU

What is light?What is light?• Light is an electromagnetic wave that consists of

time varying electric and magnetic fieldtime-varying electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to pe pe d cu a to eac ot e a d pe pe d cu a tothe direction of energy propagation .

• Who understands this?

6PHYS52 Eradat SJSU

Electric flux & Gauss’s Law

7PHYS52 Eradat SJSU

Magnetic flux & Gauss’s law

8PHYS52 Eradat SJSU

Faraday’s LawFaraday s Law

9PHYS52 Eradat SJSU

Ampere’s LawAmpere s Law

10PHYS52 Eradat SJSU

Maxwell’s contribution to the Ampere’s law

∂⎛ ⎞∫ ∫∫E

0 ,C

dl dt

μ ε ∂⎛ ⎞⋅ = + ⋅⎜ ⎟∂⎝ ⎠∂

∫ ∫∫A

EB J s

E

Ampere's circuital law:

tI d

∂∂

= ∫∫

EE

J s

a time-varying -field

or charges in motion (electric current) ,I d= ⋅∫∫A

J s

B

or charges in motion (electric current)

will generate a -field


Before MaxwellBefore Maxwell

dΦ∂∫ ∫∫

B

Faraday's induction law: a time-varying magnetic field will have an

-

1

BC

ddl dt dt

d dVρ

Φ∂⋅ = ⋅ = −

∂

⋅ =

∫ ∫∫

∫∫ ∫∫∫A

BE s

E s

electric field associated with it.

Gauss's law-electric: when there are no0

,V

d dVρε

=∫∫ ∫∫∫E sA

Gauss s law electric: when there are no

sources or sinks of the electric field within the region encompassed by a closed surface the net flux through the surface equals to zero

0,dΦ = ⋅ =∫∫ B sM A

by a closed surface, the net flux through the surface equals to zero.

Gauss's law-magnetic: there is no magnetic monopole.

∂⎛ ⎞EA ,C

dl dt

μ ε ∂⎛ ⎞⋅ = + ⋅⎜ ⎟∂⎝ ⎠∫ ∫∫A

EB J s

E B

mpere's circuital law: a time-varying

-field or charges in motion (electric current) will generate a -fieldg ( ) g


Maxwell equations; integral formBehavior of electric and magnetic fields in a medium with

,,

ε μρ J

Behavior of electric and magnetic fields in a medium with electric permitivity and magnetic permeability , in presence of free charges , and current density is explained ρby four integral equa

1 enclQd dVρ⋅ = = ←∫∫ ∫∫∫E s

tions known as Maxwell equations.

Gauss electric

0V

d dV

dA

ρε ε

←

⋅ = ←

∫∫ ∫∫∫

∫∫

E s

B

A

A

Gauss electric

Gauss magnetic

BC

d ddl ddt dtΦ

⋅ = − = ⋅∫ ∫∫A

E B s

d d

←

Φ⎛ ⎞ ⎛ ⎞∫ ∫∫E

Farady

ECC

d ddl i ddt dt

μ ε μ εΦ⎛ ⎞ ⎛ ⎞⋅ = + = + ⋅ ←⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠∫ ∫∫

A

EB J s Amper

The book has these equations in vacuum with

13

0 0,ε μelectric permitivity and magnetic permeability PHYS52 Eradat SJSU

The wave equation for the E and M qcomponents of the EM waves

M ll t t d f diff ti l f f hi ti

0

Maxwell started from differential forms of his equations. In vacuum ρ =

0

0,0

ρ

ε ε

===

J

0

0 He derived a differential wave equation for both E and B μ μ=

2 2

2

fields through decopling two of the equations: d d

+E E 2 2

0 02 2 2 d dμ ε+ =E E

2dx 0 02 2 2dy dz dtμ


Speed of the EM waves2 2 2 2d d d dE E E E

0 02 2 2 2

2 2

Wave equatuon for the Electric fields:

1Classical wave equation:

d d d ddx dy dz dt

d y d y

μ ε+ + =

=

E E E E

2 2 ,2Classical wave equation:

is speed of the wave,Comparing the two equations Maxwell concluded that speed of t

dx V dtV

=

heComparing the two equations Maxwell concluded that speed of t

12 71| | 8 8541878176 10 4 10

he electromagnetic waves must be:

With dF NV − −12 70 0 2

0 0

8

| | 8.8541878176 10 4 10

1| | 299792458 000345 2 99792458 10 /

With and Vm A

V m s c

ε μ πμ ε

= = × = ×

= = = × =0 0

| | 299792458.000345 2.99792458 10 /

| |Surprise: Speed of light??!!! S li ht i l t

V m s c

V cμ ε

= = = × =

=tiSo light is an electromagnetic wave.


Electromagnetic Waves or LightElectromagnetic Waves or Light• Light or electromagnetic wave consists of time-

varying electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction ofother and perpendicular to the direction of energy propagation.

• Light is a wave• Light is a wave• A wave has frequency

A a e has a elength• A wave has wavelength• Color of the light is d t i d b it fdetermined by its frequency


WaveWave• A self sustaining energy-carrying disturbance of a

medium through which it propagatesmedium through which it propagates.• Longitudinal wave: the medium is displaced in

the direction of motion of the wave.• Transverse wave: the medium is displaced in a

direction perpendicular to that of the motion of ththe wave.

• Why waves can propagate faster than the medium in which they propagate?medium in which they propagate?

• When a wave propagates, the disturbance advances, not the medium (Leonardo da Vinci)., ( )


Harmonic wavesHarmonic waves are smooth patterns that repeat endlesly.

They involve the sine and cosine functionsHarmonic wavesThey involve the sine and cosine functions.

is a mathematical expression that represnts the wave mothion in space and timeWavefunction :the wave mothion in space and time. Wavefunction of the simple harmonic waves are and

functionssin

cos

( ) functions.

cos y A kx tω φ= − +

cos

( ) siny A kx tω φ= − +


Information hidden in a wave function( )

Amplitude Initial PhasePhase

cos or siny A kx t y A kx tω φ ω φ⎛ ⎞

= − + = − +⎜ ⎟⎜ ⎟⎝ ⎠

2 Wave nuumber: number of wavelengths in unit length

2

k πλ

=

2= Wavelength: Length of one complete cyclek

Frequency: nuV cf

πλ

mber of complete cycles per second0

Frequency: nufλ λ

= = mber of complete cycles per second

2 Angular frequency: the amount of phase accumulated/secondfω π=

01 Temporal period: Amount of time it takes to

complete a cycle In vacuum =

Tf V c

V c

λλ

λ λ

= = =

= 0complete a cycle. In vacuum =V c λ λ=


Index of refractionIndex of refraction I d f f ti Speed of light in vacuumIndex of refraction

p f g

Speed of light in material

c

=

cnV

Since

=

> We allways have:

SinceSpeed of light in vacuum Speed of light in any materialWe allways have:

1n ≥

PHYS52 Eradat SJSU 20

The electromagnetic spectrumThe electromagnetic spectrum


Wavefronts Spherical wavefrontWavefronts• Wavefront: loci of the adjacent

points on the wave with the

Spherical wavefront

points on the wave with the same phase

• In homogeneous (no densityIn homogeneous (no density fluctuations) and isotropic (same material) media wavefronts do not change as wave propagates.

Direction of propagation

• Most common wavefronts are planar, spherical and cylindrical

Planer wavefront

cylindrical 22PHYS52 Eradat SJSU

Optical rays• Optical rays: (imaginary) lines drawn

perpendicular to the wavefronts. Rays

• Rays show direction of propagation.In homogeneous and isotropic• In homogeneous and isotropicmedia the rays are straight lines.

• Isotropic means identical values of aIsotropic means identical values of a property in all directions. Homogeneous means material or system that has the same properties in any direction. In optics this means wave propagation is the same in allwave propagation is the same in all directions. 23PHYS52 Eradat SJSU

Geometrical optics vs. physical optics

• Rays: geometrical opticsRays: geometrical optics • Wavefronts: physical optics

G i l i f iλGeometrical optics: feature sizes Or the accuracy required can be achieved by

λ <<

geometricl treatment.Physical optics: feature sizesλy pabout -100Or a very high accuracy is demanded

λ λOr a very high accuracy is demanded


Reflection & RefractionReflection & Refraction• When light hits interface of two dielectric

(transparent) media depending on the(transparent) media depending on the – angle at which it hits – ratio of the indices of refraction

it may be – reflected– reflected – refracted

Scattered– Scattered– or a combination of all happens

Wh t b ti ?• Why not absorption?25PHYS52 Eradat SJSU

Reflection & Refraction• When light hits interface• When light hits interface

of two dielectric (transparent) media it(transparent) media it may be – reflectedreflected – refracted


Specular reflection at polished surfaces Diff d fl ti t h fDiffused reflection at rough surfaces

polished to ~ to /10 or even /20λ λ λ

polished to >λ


Laws of Reflection & RefractionAKA Snell’s Laws

These laws are results of experimental studies but palso can be proven using the wave equations and boundary conditions (the proof is outside relm ofboundary conditions (the proof is outside relm of this course).


Laws of Reflection & RefractionAKA Snell’s LawsAKA Snell’s Laws

1) The incident (ray), reflected, and normal to the surface are all in one plane thatis perpendicular to the interface.2) L f fl ti2) Law of reflection: Angle of incidence = Angle of reflecction

θ θ

3) Law of rr aθ θ=

efraction: the reflected and f t d b t i t f f trefracted beams at an interface of two

dielectrics follow this relationship:

i iθ θan sin sina b bnθ θ=29PHYS52 Eradat SJSU

Reflection and refractionReflection and refraction• Find the direction of reflected and refracted rays

in this figurein this figure.060aθ =0

0

60

49.3r

b

θ

θ

=

=


Index of refraction and speed of the lighti iθ θsin sin

sin sin

In general: If

If

a a b b

a a b b

n na b a b a b

n na b a b a b

n n V V

n n V V

θ θ

θ θ

θ θ

θ θ

=

=

> ⎯⎯⎯⎯⎯⎯→ < → <

< ⎯⎯⎯⎯⎯⎯→ > → >What if one of the media is air or vacuum?

sin sinsinair air glass glass

i

n nθ θθ

= ⎫⎪⎬ sin sinl l l

cn θ θ= =sin1 air

airnθ⎬

= ⎪⎭sin sin

sin sin

glass glass glassglass

air glass air glass air glass air glass

nV

V V n n

θ θ

θ θ θ θ→ > → > → > → >

Allways : 1material

cV

>


Index of refraction and wavelength

0 c V cf f nV

λλ λ λ

= → = → = =0

In a mediumIn Vacuum

Vλ λ λ

0 01since allways or n nλ λ λ λ> → > =


Index of refraction in the eyeIndex of refraction in the eye• Wavelength of the light from HeNe laser

i th i i 633 I d f f ti f thin the air is 633. Index of refraction of the aqueous humor in the eye is 1.34.

• What is the wavelength of the HeNe light in the eye?

• What is the speed of this light in the air and eye?y

• What is the frequency of this light in the air and eye?air and eye?


Which statement is trueWhich statement is true

• Color of a wave is determined by itsColor of a wave is determined by its wavelength

True– True– False

C l f i d t i d b it• Color of a wave is determined by its frequency

T– True– False


Total internal reflectionaIf n then the snell's law suggests an interesting effect.bn>

R2

11

sin sin sin sinaa a b b a b

b

nn nn

θ θ θ θ≤

>

= → =

nbna

R2

r2

1

0sin 1 90The only way to have the equation work is to have: a aθ θ

>

< → <a

Θ1 Θ2’

r r’1

Θcrit θ>θcritThe largest angle for which the refracted rays still exist is called the critical angle θ

Na>nb

R1 R’1

r11

0sin 1 90 .

cis called the critical angle .

At we have or

a c

b b

θ

θ θ

θ θ

=

= =sin 1 90 .

c

or For the light is totally reflected back into its first environment and there is not refraction.

b b

a

θ θθ θ>


This is called total internal reflection or TIR.

Applications of the total internal fl i (TIR)reflection (TIR)

Fiber optics: revolutionized telecommunicationWhy light does not undergo total internal

Porro prism for changing direction of propagation

By 1800 Used in camerasy g greflection at the end of the fiber? By 1800. Used in cameras

And binoculars 36PHYS52 Eradat SJSU

A twice reflected rayA twice reflected ray• A ray traveling on a

surface perpendicular p pto two perpendicular mirrors is shown. What is the direction of final ray emerging yy g gfrom the mirrors.

• Measure the angleMeasure the angle with respect to positive direction of y axisdirection of y axis.


Chapter 33 Summary I

Typo in the bookTypo in the bookλ=λ0/n


Chapter 33 Summary II


Electromagnetic spectraElectromagnetic spectraA superposition of many waves with different wavelengths or frequencies with a speed of c forwavelengths or frequencies with a speed of c for all of them in vacuum


Wavelength dependence of the refractive index (Dispersion)refractive index (Dispersion)

Dispersion is caused by the p yvariation of speed of light (index of refraction) in the

di i h fmedium with frequency

High dispersion

Almost dispersion free.


Application of dispersion: Which material is the best choice for a spectrometer?the best choice for a spectrometer?


Is there a pot of gold at the end of i b ?rainbow?

• Rainbow is caused byRainbow is caused by reflection and refraction of the sunlight from rein drops due to di i ff tdispersion effect.


Electromagnetic wavesElectromagnetic waves• Composed of oscillations p

of electric and magnetic fields perpendicular to each other in a plane pperpendicular to the direction of propagation of the wave (a

H d k i l i d(

transverse wave)• For unpolarized light the

direction of E field is not max( , ) cos( )E x t JE kx tω= −

How do we know a wave is polarized when we see equation of the wave?

direction of E field is not fixed. It rotates in yz plane (usually we detect electric field)

max

max

( , ) ( )

( , ) cos( )B x t kB kx tω= −

electric field). This light is polarized in y direction


How to recognize a l i d li hpolarized light

• Once a wave is polarized pit only oscillates in a fixed direction (let’s say y)

• We can use filters toWe can use filters to allow only certain oscillations to pass

• Or we can produce• Or we can produce polarized light from beginning by imposing restrictions on therestrictions on the oscillations of the electric charges that produce the lightlight.


How to polarize lightHow to polarize light• Radio waves produced by antennas are usually polarized

along the antenna length. • Light from an incandescent lamp is unpolarized due to the

random orientation of the molecules that produce the light.g

• Dichroism: selective absorption of light based on direction of the oscillation of E field.

• There is always loss associated with polarization process• There is always loss associated with polarization process. • Ideal polarizer is the one that passes 100% of the

originally polarized light (all of our filters will assumed to b id l)be ideal).


DichroismDichroism


Intensity of the polarized light produced from l i d li ht i id l l ian unpolarized light using an ideal polarizer

• Transmitted light intensity is half of the incidentTransmitted light intensity is half of the incident light

I /2I0/2

II0


Second polarizer or analyzerp y2

Intensity of an electromagnetic wave is proportional to square of its amplitude

I E∝

2max

Malus's law (1809), polarized light passing through an analyzer is:

cos I I φ=

Problem: What would be intensity after the second polarizer if incident intensity was I0 and the angle between two polarizer was 300? 49PHYS52 Eradat SJSU

Polarization by reflectionPolarization by reflection• Polarization angle or Brewster (1812) angle is an angle of

incidence that causes the reflected light be completely polarized in the direction perpendicular to the plane of incidence. For Brewster p p pangle reflected and refracted rays are perpendicular to each other.


Brewster’s lawBrewster s law90

p b

b p

R R

θ θ

⊥

= −

sin sin sin(90 ) cos

Brewster's law for the polarizing angle

p

a p b b b p b pn n n nθ θ θ θ= = − =

sin cos

tan Berwester angle

a p b p

bp

n n

n

θ θ

θ

=

= ← gpan


ExampleExample• Consider a swimming pool. At what angle of reflection the sun

li h i l l l i d? (53 10) Wh i h l flight is completely polarized? (53.10) What is the angle of refraction for the corresponding transmitted ray? (36.90)

• How about the light from a floodlight inside the pool? (36.90)


Circular and Elliptical Polarization( ill b d i h 3 )(will be covered in chapter 35)

• Superposition of two waves:p p• Zero phase difference results linear polarization• π/2 phase difference results circular polarization

(clockwise: right and counterclockwise: left)(clockwise: right and counterclockwise: left)• Other phase difference results in elliptical polarization


Chapter 33 Summary IIIChapter 33 Summary III


Chapter 33 Summary IVChapter 33 Summary IV


Scattering of lightScattering of lightIntensity of scattered light is proportional to

144

1the 4th power of frequency!! scatteredI fλ

∝ ∝


Why sky is blue? Why sunsets are red? Why clouds are white? Why sky is darker viewed y yfrom some angles by Polaroid sunglasses?

4 1I f• It is all due to scattering of light from the air molecules.

S tt d li ht t i i t l 9 4 ti bl

44scatteredI f

λ∝ ∝

• Scattered light contains approximately 9.4 times more blue light as red light.

• Whatever is not scattered from the air molecules is transmittedtransmitted.

• What we see in the sky during day time is more the scattered light

• What we see in the evening is more the transmitted lightWhat we see in the evening is more the transmitted light• Sunlight is un-polarized. The scattered light that reaches our

eyes can be polarized (How?)• Clouds are thick and eventually scatter all the elements of the y

sun’s spectrum57PHYS52 Eradat SJSU

Huygens’ Principle (1678)R f ti d R fl ti b d f hRefraction and Reflection based of wave phenomena

• If we know shape of the pwavefront at time t, we can use the Huygens’ principal to find the shape of the pwavefront at t+dt

• Every point of a wave front may be considered asmay be considered as source of a secondary wavelets that spread out in all directions with ain all directions with a speed equal to the speed of propagation of the

New wavelets tangent to theSurface of the original wave front

wave.58PHYS52 Eradat SJSU

Reflection based on Huygens’ P i i lPrinciple

AQ OP vt= =

a r

AQ OP vtθ θ=


Refraction based on Huygens’ P i i lPrinciple

bAB v t=

Wave frontsin

b

a

a

QO v tv tθ

=

sin

sin

aa

bb

AOv t

θ

θ

=

=Ray direction

sin

sinsin

b

a a b b

AOv v ncv v c n

θ

θθ

= = =

Normal to the surface

θαsin

sin sin Snell's Law

b b b a

a a b b

v v c nn n

θθ θ=

Snell's Law60PHYS52 Eradat SJSU

SummarySummary


ProblemsProblems

• 33.11 Show that the33.11 Show that the angle between two reflected beams is twice the angle A between the two

fl ti freflecting surfaces


ProblemsProblems

• 33.40 How far is the33.40 How far is the key from the edge of the pool?


ProblemsProblems

• 33.55 Show that the33.55 Show that the angle of deviation of a prism when the light is passing through symmetrically is

sin sin2 2

A Anδ+=


ProblemsProblems1. Prove that θa= θ‘

a2 P h hi i f2. Prove that this is true for any

number of different parallel plates.

3. Prove that the lateral O

displacement d of the emergent beam is given by the relation 1.

4 A ray of light is incident at an4. A ray of light is incident at an angle of 66.0 degrees on one surface of a glass plate 2.40 cm thick with an index of refraction 1 80 The mediumrefraction 1.80. The medium on either side of the plate is air. Find the lateral displacement between the incident and emergent rays

'

'

sin( ) (1)cos

a b

b

d t θ θθ−

=incident and emergent rays. b


Chapter 33Chapter 33 - erbion.com 33.pdf · – X-ray optics – Y-rays PHYS52 Eradat SJSU 3. What is light? It' bi d it' l ! N ! It' S !It's a bird, no, it's a plane ! No ! It's

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