光的干涉和繞射實驗

雙狹縫干涉

d λd λ

d

d

Diffraction≡The bending of a wave around the edges of an obstacle

兩個波 (波長相同 )的疊加

2

1 (x) sin(kx)

(x) sin(kx + )

y

y A

A

0°

2

1 (x) sin(kx)

(x) sin(kx + )

y

y A

A

180°

2

1(x) sin(kx

(x) sin )

)

(kx

y A

y A

1 2 (x)(x)

2 s

(x)

in(kx)

A

yy y

1 2(x) ((x)

0

x)

yyy

雙狹縫干涉sin ; 0, 1, 2...d n n 建設性干涉 破壞性干涉

1sin ( ) ; 0, 1, 2...

2d n n

dd

Electromagnetic Wave(電磁波 )

ˆ(x, ) cos (kx - ) ��������������E t E t j0

ˆ(x, ) cos (kx - ) ��������������B t B t k0

EM WAVE 24.3Active Figure

20 0

(Intensity)

1

2

; 2 ; 2

電磁波的強度

k f c

I c E

fk

1 1 0 1

2 2 0 2

1 2

2

0

( , ) sin( )

( , ) sin( )

1

2

E l t E kl t

E l t E kl t

E E E

I c E

合

合 振幅

0

20 0

( , ) sin( )

2 ; 2 ;

1

2

E x t E kx t

k f c fk

I c E

0 1 0 2sin( ) sin( )E E kl wt E kl wt 合

0 2 10 1 1sin( ) sin{ ( )}E E kl wt E kl kt klw l 合

2 1( ) 2

sin 2

sin

2

; 0, 1, 2...

k l l lk

n

n

d n

d n

建設性干涉

0 1

2

max 0 0

2 sin( )

12

2

E E kl wt

I c E

合

1 1 0 1

2 2 0 2

1 2

2

0

( , ) sin( )

( , ) sin( )

1

2

E l t E kl t

E l t E kl t

E E E

I c E

合

合 振幅

0

20 0

( , ) sin( )

2 ; 2 ;

1

2

E x t E kx t

k f c fk

I c E

0 1 0 2sin( ) sin( )E E kl wt E kl wt 合

0 2 10 1 1sin( ) sin{ ( )}E E kl wt E kl kt klw l 合

2 1( ) (2 1)

sin (2

; 0, 1,

2 1)

2..1

sin ( )2

.

k l l l n

d

d n

n

n

k

破壞性干涉

min

0

0

E

I

合

雙狹縫干涉sin ; 0, 1, 2...d n n 建設性干涉 破壞性干涉

1sin ( ) ; 0, 1, 2...

2d n n

dd

雙狹縫干涉 ( 測量 )

sin ; 0, 1, 2...d n n 建設性干涉

n

n

ysin tan

Dy

D

; 0, 1, 2...

d n nd

D

yn

雙狹縫干涉 ( 測量 )

n

n+1

n+1 n

n+1 n n+1 n

D

( ) D

----------------------------

yn

yn+1 1

y y

-------------------

( )( 1

y y y

) D

( ) ( )

D

y

D

第 個亮紋

第 個亮紋

d

n

d

n

n n

d

d

d

d

D

yn

若兩個連續亮紋分別為

n+1 ny y( ) y

D Dd d

d

D

Δy

D ≈ 300cm

雙狹縫干 ( 繞 ) 涉紋

5Δy

Diffraction Grating( 多狹縫 )

• The condition for maxima is

• The integer n is the order number of the diffraction pattern

Bright

sin ; 0, 1, 2...d n n

n+1 ny y( ) y

D Dd d

D

d

D ≈ 60cm

單狹縫繞射 ( 頭髮 )

dark darkiy

sin tanL

2y1

1y=

L a

中央亮帶

L ≈ 100cm

暗紋

暗紋

暗紋

暗紋

Dark(

in

)

sa n 暗紋

sin

D

2 2

sin

ark( )

a

a

暗紋

LASER經由輻射的激發放射放大光

• Light Amplication by Stimulated Emission of Radiation

• Same frequency ( 頻率相同 )

• Same direction ( 方向相同 )

• Same phase ( 相位相同 )

• Same polarization ( 極化相同 )

光與物質的作用 : 吸收 Absorption

ΔE= h f

自發放射 Spontaneous Emission

ΔE= h f

激發放射 Stimulated Emission• Same frequency Same direction • Same phase Same polarization

激發放射 Stimulated Emission

自發放射 激發放射 激發放射 激發放射 激發放射

• Same frequency Same direction • Same phase Same polarization

Population Inversion

• Same frequency Same direction • Same phase Same polarization

Energy Levels, He-Ne Laser

• This is the energy level diagram for the neon

• The neon atoms are excited to state E3*

• Stimulated emission occurs when the neon atoms make the transition to the E2 state

• The result is the production of coherent light at 632.8 nm

20.61 eV 20.66 eV

18.70 eV

紅寶石雷射

Properties of Laser Light

• The light is coherent– The rays maintain a fixed phase relationship with one

another– There is no destructive interference

• The light is monochromatic– It has a very small range of wavelengths

• The light has a small angle of divergence– The beam spreads out very little, even over long

distances

Stimulated Emission

• Stimulated emission is required for laser action to occur

• When an atom is in an excited state, an incident photon can stimulate the electron to fall to the ground state and emit a photon

• The first photon is not absorbed, so now there are two photons with the same energy traveling in the same direction

Stimulated Emission, Example

Stimulated Emission, Final

• The two photons (incident and emitted) are in phase

• They can both stimulate other atoms to emit photons in a chain of similar processes

• The many photons produced are the source of the coherent light in the laser

Necessary Conditions for Stimulated Emission

• For the stimulated emission to occur, there must be a buildup of photons in the system

• The system must be in a state of population inversion– More atoms must be in excited states than

in the ground state– This insures there is more emission of

photons by excited atoms than absorption by ground state atoms

More Conditions

• The excited state of the system must be a metastable state– Its lifetime must be long compared to the

usually short lifetimes of excited states– The energy of the metastable state is

indicated by E*– In this case, the stimulated emission is likely

to occur before the spontaneous emission

Final Condition

• The emitted photons must be confined– They must stay in the system long enough to

stimulate further emissions– In a laser, this is achieved by using mirrors at

the ends of the system– One end is generally reflecting and the other

end is slightly transparent to allow the beam to escape

Laser Schematic

• The tube contains atoms– The active medium

• An external energy source is needed to “pump” the atoms to excited states

• The mirrors confine the photons to the tube– Mirror 2 is slightly transparent

Energy Levels, He-Ne Laser

• This is the energy level diagram for the neon

• The neon atoms are excited to state E3*

• Stimulated emission occurs when the neon atoms make the transition to the E2 state

• The result is the production of coherent light at 632.8 nm

Laser Applications

• Laser trapping

• Optical tweezers

• Laser cooling– Allows the formation of Bose-Einstein

condensates