1

1. the Doppler effect

2. the nature of light, wave-particle duality

3.Light as electromagnetic waves

4.Coherent light, Interferences of light

2

Optical Path Length（光程）

Path length: i ii

r n r0 2

r

f

light

0 is the wavelength of light in vacuum.

3

Young’s Double-Slit Experiment （杨氏双缝试验）

4

Optical Path Difference in Double-Slit Experiment

2 1 siny

r r d dL

5

2 2 2 22 1

2 2

( ) ( )2 2

2 2 [( ) ( ) ]2

d dr r L y L y

d dy yL

L Lyd

L

yd

L 2for 1

dy

L

2for 1

dy

L

6

Case 1:

, 0, 1, 2, m m

(or )L

y md

interfere constructively

bright fringes（亮纹）

Case 2:

1( ) , 0, 1, 2,

2m m

1(or ( ) )

2

Ly m

d

interfere destructively

dark fringes（暗纹）

7

, 0, 1, 2, m m

Order Number of Bright Fringes（亮纹的级数）

y = 0, central bright fringe （中央亮纹）

m = 0:

zeroth-order maximum （零级极大）

m is called order number.

y = λL/d, first-order maximum

（ m 称为级数）

( 一级极大 )1m

8

Spatial Distribution of the Interference Fringes

m

Lx m

d

Bright Fringes

Dark Fringes m 1

( )2

Ly m

d

1m m

Lx x

d

1m m

Ly y

d

msin md

m

1sin ( )

2m

d

angular positions

（干涉条纹的空间分布）

9

Intensity Distribution of the Double-Slit Interference Pattern

2 21 2 1 2

22 cosA A A A A

；

1 2 1 2

22 cosI I I I I

（双缝干涉图样的强度分布）

10

Monochromatic light （单色光）

As discussed above.

White light （白光）

All bright fringes except the central one are chromatic.

About the Light Source

m

Ly m

d

The position of the bright fringes:

（除了中央亮纹，其他亮纹都是彩色的）

11

Question

If there exists medium in space, the refraction

index of which is n, what are the positions of the

bright and dark fringes?

2 1( ( ) )nyd

n r rL

12

Lloyd’s Mirror（劳埃德镜）

Dark fringe is found at p’ due toπ-phase shift.

2 1( )2

n r r

13

Fresnel’s Double-Mirror（菲涅尔双镜）

1M

2M

Interference pattern can only be observed in dark zone.（只有阴影区域可以观察到干涉图样）

14

Interference in Thin Films（薄膜干涉）

1 2(air) (film)n n

film

air

15

21 2

2 2 22 1

22 tan ' 2 cos '

2

2

sincos

sin2

' 2aa

a

n t i

t

n tt i n i

n n i

i

Lenses do not influence the optical path difference（透镜不引起附加的光程差）

16

2

1 2 cos ' ( )

2

m

or n t i m

interfere constructivelybright fringes

2

1( )

2 2 cos '

m

or n t i m

interfere destructivelydark fringes

interferences of equal inclination （等倾干涉）

'i i

17

L

P

Planar light source

mirror

Thin film

lens

Viewing screen

PatternBright/dark fringes

18

The Interferences of Equal Inclination（等倾干涉）

1. The fringes are rings with a common center

2. The distance between the adjacent fringes is not uniform

3. The order number reaches its maximum at the center.

（干涉条纹是同心圆环）

（相邻条纹的间距不相等）

（中央条纹的级数是最大的）

2

12

1 2 cos ' ( )

2

cos ' cos '2m m

m or n t i m

i in t

19

Interferences of Transmission（透射光的干涉）

i

i

1

23

2 2 22 12 sint n n i

For a given incident angle, if the reflected light interfere toproduce bright fringes, then the transmitted light produce darkfringes.

20

Interference in a Wedge-shaped Film

21

hl

S

Wedge with very small θ

Light source

lens

mirror

microscope

22

2 1

2 1

1n n , 2

21

n n , 22

nh

nh

1n

2n

1( )

2

m

m

bright fringes

dark fringes

23

Discussions on Wedge-Shaped Film

Case1: h = 01

2 dark fringes

Case 2: 2

1( )

2 2m h m

n

bright fringes

height difference between adjacent bright fringes:

22h

n

So, the distance between two adjacent bright fringes is

2 2tan 2 tan 2

hx

n n

24

The total number of bright fringes which can be observed thus can

be obtained as

lN

x

And it is easily to find the fringes are spaced uniformly.

（易得，条纹是均匀分布的）

（在劈尖上能够观测到的亮条纹的条数可以计算如下）

The interference in a wedge-shaped film is called interference of

equal thickness for the obvious reason.

（劈尖上的干涉被称为等厚干涉）

25

Quick Quiz

What if?

(1) What happens to the fringes if the upper (lower) surface of

the wedge-shaped film moves upward a little.

(2) What happens if the angle of the wedge-shaped film increases.