電磁波基本性質實驗

•Bragg Diffraction ( 布拉格繞射 )

•Fiber Optics( 光纖光學 )

Bragg Diffraction ( 布拉格繞射 )

• 由相鄰兩晶面所反射出來的電磁波之波程差若為 2dsin ，其中 d 為晶面距離， 為入射波與晶面之間夾角，則建設性干涉的條件為波程差恰好為波長 λ 的的的的

2dsin = nλn = 1, 2, 3 …

布拉格定律 (Bragg’s Law)

Diffraction of X-Rays by Crystals

Laue pattern

Laue Pattern for Beryl(Beryllium aluminum silicate)

Laue Pattern for enzyme Rubisco

Fig. 27-27, p. 920

Crystalline structure of Nacl

x

y

z

Cl-

Na+

晶面之指數 (Miller indics)

• 晶面上的三點決定晶面之指數 (Miller indics)

• 三個晶軸與晶面交接點 ( 截距 )

• 取截距倒數• 化成最小整數比

( 1 0 0 ) 平面

x

y

z

( 1 0 0 ) 平面

( 2 0 0 ) 平面

1 1

)

)

(

(

1

2

2

2

2

0 0

00

平面為例

平面指數

平面與晶軸截距

倒數

1 1

21

2 1

(2 1 0)

(210)

平面為例

平面指

平

數

面與晶軸截距

倒數

4 1 2

1 1 1 4 2

1 4 2

(

(142)

142)

平面與晶 軸截距

平面為例

平面

倒數

化成 比指數

最小整數

x

y

z

( 1 1 0 ) 平面

( 1 1 1 ) 平面

Fig. 27-28, p. 920

2dsin = nλ n = 1, 2, 3 …

Bragg Diffraction ( 布拉格繞射 )

d

2dsin = nλ n = 1, 2, 3 …Grazing angle

接收器

接收器

發射器

(210) 面

12

Fiber Optics( 光纖光學 )

• 利用細長柔軟纖維 ( 由玻璃、塑膠或其他透明材料製成 ) 傳送光信號的技術

• 光波由纖維絲的一端進入後，由於全反射作用，將纖維絲方向傳輸而不從周壁逸出

Snell’s Law of Refraction

• Snell’s Law

• n1 sin θ1 = n2 sin θ2

– θ1 is the angle of incidence

– θ2 is the angle of refraction

n1

n2

• A phenomenon called total internal reflection can occur when light is directed from a medium having a given index of refraction toward one having a lower index of refraction

Total Internal Reflection

Critical Angle

• There is a particular angle of incidence that will result in an angle of refraction of 90°– This angle of inciden

ce is called the critical angle, θC

21 2

1

sin C

nfor n n

n

Optical Fibers

• An application of internal reflection

• Plastic or glass rods are used to “pipe” light from one place to another

• Applications include– medical use of fiber optic

cables for diagnosis and correction of medical problems

– Telecommunications

Optical Fibers, cont

• A flexible light pipe is called an optical fiber

• A bundle of parallel fibers (shown) can be used to construct an optical transmission line

R-d dsin θ 1

R R

sin

改變

時

a

a

a

θ sinθ

R-dsinθ

R R ,

-dsi

R

R

R

nθ 1

R >

R <

R

f air

f

f

n n

n

n'

'

'

'

使微波在光纖中

若微則

則微波往外逸

波在光纖中

全反射

出接收器

傳遞訊號

若的訊號降低

R-d

θ' θ>

接收器

發射器

c

R-d dsin θ 1

R Rd

θ R

θ

R

θ (critical angle)

<

隨著

當 微波往外逸出接收器

減少 增加 變小

的訊號降低

-

R

R dfn'

'

• End of the Lecture

Optical Fibers, cont

• A flexible light pipe is called an optical fiber

• A bundle of parallel fibers (shown) can be used to construct an optical transmission line

Construction of an Optical Fiber

• The transparent core is surrounded by cladding– The cladding has a lower n

than the core– This allows the light in the

core to experience total internal reflection

• The combination is surrounded by the jacket

Multimode, Stepped Index Fiber

• Stepped index comes from the discontinuity in n between the core and the cladding

• Multimode means that light entering the fiber at many angles is transmitted

Multimode, Graded Index Fiber

• This fiber has a core whose index of refraction is smaller at larger radii from the center

• The resultant curving reduces transit time and reduces spreading out of the pulse

Optical Fibers, final

• Optical fibers can transmit about 95% of the input energy over one kilometer

• Minimization of problems includes using as long a wavelength as possible

• Much optical fiber communication uses wavelengths of about 1300 nm.

Total Internal Reflection (Critical Angle)

• There is a particular angle of incidence that will result in an angle of refraction of 90°– This angle of inciden

ce is called the critical angle, θC

21 2

1

sin C

nfor n n

n

R-d dsin θ 1

R R

sin

改變

時

a

a

a

θ sinθ

R-dsinθ

R R ,

R-dsinθ 1

RR

R-d

f air

f

f

f

n n

n

n

n

使微波在光纖中傳遞訊號R-d

θ' θ> 產生 Total Internal Reflection

c

R-d dsin θ 1

R Rd

θ R

θ

R

θ (critical angle)

<

隨著

當 微波往外逸出接收器

減少 增加 變小

的訊號降低

Fig. 25-28, p. 856

Fig. 25-29, p. 857

Fig. 25-30, p. 857