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Ch22 Wave Optics講者： 許永昌 老師

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ContentsModels of light:

Wave ModelRay ModelPhoton Model

Double-slit interference ( 實驗 7)The diffraction gratingSingle-Slit diffraction ( 實驗 7)

Choosing a model of lightInterferometers ( 實驗 10)

Michelson interferometerHolography

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Models of light ( 請預讀 P670~P672)

The study of light is called optics ( 光學 ).Models of light

Wave Model: Electromagnetic wave. Interference

Diffraction Typically, D << 1 mm

Ray Model: Particle-like Lens, Mirrors,… Typically, D >> 1 mm

Photon Model: Photons have both wave-like and particle-like properties. Photoelectric effect, QIS,… Very low illumination.

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ActionPurpose: Get the feeling about the wave and ray

nature of light.Objects:

A laser penAn aerosol A narrow single slit

Action:Spraying an aerosol into the laser beam.Send the laser beam through single slit.

Light travels in a straight line? Light is a wave? Edge effect?

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Double-slit interference ( 請預讀P672~P678) It is a strong evidence of the wave nature of light.Easy to analyze. In this part, you should learn

The configuration of double-slit experiment The construction and destruction

Fringe spacing Intensity vs. energy conservation

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Double-Slit Interference (continue)Model: ( 做很多假設喔 )

Dr dsinq~dq.On screen: y=Ltanq~Lq.

On the screen:Dnet=D1+D2.D1=asin(kr1-wt+f0)=asin(f1)

Bright fringe (Constructive): D1=D2.kDr=2 p m. Dr=ml.We get ybright=mlL/d.

Fringe spacing=lL/d.

r1

r2

L

d

q

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Double-slit interference (continue)Intensity: I= ½ ce|E0|2.

此處 a=E0.E0 為 的振幅，如果它是由 n 個波疊加的

話。Bright fringe: A(ybright)=2a.

Imax=4I0.

Dark fringe: A(ydark)=0.Imin=0.

Average: 2I0.

1 2 3 ... nE E E E E

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MathematicsPhasor diagram (P1115, Ch36)D1=asin(kr1-wt+f0)=asin(f1)

It is related to the y component of a vector.

If the frequencies of D1 and D2 are the same,i.e. Df=constant,Dnet=Asinf, too, where A is the length of the net vector.

f1(t)

aD1

1 2 1 2 yD D v v

x

y

此處的 x,y 是對 phasor diagram 在講，而不是對描述光干涉空間在講，請小心。

aD1

x

y

f1(t)

f2(t)

a

D2 A

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Double-slit interference (final)From this figure, we can find that

A=2acos(Df/2). Substitute Eqs. shown in P6 into this equation, we

get

Intensity:

Df

2 cosd

A a yL

204 cos

dI I y

L

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HomeworkStudent Workbook:

1, 2, 4

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ExerciseHow about triple-slit interference?

Please use the phasor diagram to find the positions of dark fringes. Hint: Df=?

How about the positions of bright fringes?

d

d

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The diffraction grating ( 請預讀P678~P680)

In this part, you should learnThe configuration of

diffraction and reflection grating

The construction and destruction Order of diffraction

Intensity vs. energy conservation

130 50 100-2

-1

0

1

2The diffraction grating (continue)Df=dsinq.Constructive:

Df=2pm. ybright=mlL/d

( 由圖上可見，其實 qbright 並不小，因此，這近似有點不切實際。因此，課本只寫到 dsinqbright=ml.)

A=Na.Imax=N2I0.

Destructive: NDf=2pm & mm’N.A=0.Imin=0.

Code: grating.m

~lL/d

2 L

Nd

I0N2

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MathematicsBased on phasor graph

Therefore, destructive interference is happened at NDf=2pm & mm’N.

Based on complex variable:Exp(if)=eif=cosf+isinf.

所以，它的虛部即為我們的波函數。Properties:

Exp(a+b)=exp(a)exp(b), a,b

Re(eif)

Im(eif)

11 2

1 1

12

2 1

Im ... Im 1 ...

1Im 1 ... Im .

1

N

i

i t i Nii i i inet

iNi t i tN

i

r e

D ae ae ae ae e e e

eae r r r ae

e

數學上的進化 :sin(kx-wt+f0) sin(f)y component of vector (phasor graph)complex variable.

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HomeworkStudent Workbook

5, 7

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Single-Slit diffraction ( 請預讀 P681~P684)

In this part, you should learnThe configuration of single-

slit diffraction.Huygens’ Principle

Point sources: Each point on a wave front is the source of a spherical wavelet that spreads out at the wave speed.

At a later time, the shape of the wave front is the line tangent to all the wavelets.

Intensity

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Mathematics

where Df=kDr=kb/N sinq, a= E0/N.

Intensity:

Angles of dark fringe: bsinq=ml , m0, q[- p /2 , p /2 ].

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lim Im .1

iNi t

net iN

eD ae

e

0

0sin0

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sin sin sin sin1

lim lim .sin1 sinsin

iN

net iN N

b bEe

A D a Ebbe N

N

2

0 2

sin sin.

sin

b

I Ib

0 1

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

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The Ray and Wave models of light( 請預讀 P685~P687)

Angle q1 locates the first minimum in the intensity.The angle q1 of a single-slit is sin-1(l/b).The angle q1 of a circular aperture is 1.22l/D where D is

the diameter of this circular opening.Therefore,

When l<<D, q1 0 Ray optics.When l~D, q1 700 Wave optics.

Can we define a critical diameter betweenthese two model?Central maximum width: W2.44lL/D.

Dc=W 2.44lL/Dc.

When l~500 nm, L~ 1 m, we get Dc~ 1 mm

2.44 .cD L

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HomeworkStudent Workbook

8, 9, 10, 11

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Interferometers ( 請預讀 P687~P690)

A device that makes practical use of interference is called an interferometer.It can be used to measure the

wavelength. Constructive: Dr=ml. We can get

Sound: Acoustic interferometerLight: The Michelson

Interferometer. It also can be used to measure the

index of refraction n of gas.

2.L

m

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Holography ( 請預讀 P690~P691)

Holography is an important application of Wave Optics.

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HomeworkStudent Workbook

13, 14Student Textbook

49請製作 terms and notation 的卡片