Download - CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

Transcript
Page 1: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

1

CHAPTER 26 INTERFERENCE AND DIFFRACTION

INTERFERENCE

CONSTRUCTIVE

DESTRUCTIVE

YOUNG’S EXPERIMENT

THIN FILMS

NEWTON’S RINGS

DIFFRACTION

SINGLE SLIT

MULTIPLE SLITS

RESOLVING POWER

Page 2: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

2

IN PHASE 1800 OUT OF PHASE

Page 3: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

3

OR THE BOOKS DISCRIPTION

CONSTRUCTIVE INTERFERENCE

Page 4: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

4

DESTRUCTIVE INTERFERENCE

Page 5: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

5

When two waves arrive at a point where path

differences from the sources differ by one

wavelength, two wavelengths, three wavelengths,

etc. there will be constructive interference.

Or mathematically:

�� −�� = ��ℎ���� = 0,±1,±2,±3,….

Page 6: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

6

When two waves arrive at a point where path

differences from the sources differ by ����������ℎ, ����������ℎ, ����������ℎ, ���. (Or half integer number of wavelengths) there will

be destructive interference.

Or mathematically:

�� −�� = �� +��! �

Where ℎ���� = 0,±1,±2,±3,….

Page 7: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

7

Many ways to produce two rays of coherent light.

Page 8: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

8

Consider path differences

"��ℎ#$%%������ = #&$�'

Page 9: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

9

Constructive Interference

#&$�' = �� ℎ���� = 0,±1,±2,±3,….

Destructive Interference

#&$�' = �� + ��! �

ℎ���� = 0,±1,±2,±3,….

Page 10: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

10

We can obtain the distance ( a bright line is below

(or above) the center of the screen.

Use

Page 11: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

11

If ) ≫ #

tan ' ≈ ()

Therefore

( = ) tan '

And for the �/0 bright line

(1 ≈ ) tan '1

For small angles

tan ' ≈ sin '

Therefore

(1 ≈ ) sin '1

Page 12: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

12

Use this with

#&$�' = ��

Or

&$�'1 = ��#

To get

(1 ≈ )��#

ℎ���� = 0,±1,±2,±3,…

This is the equation that Young used to measure

the wave length of light.

Page 13: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

13

As was said many ways of producing two rays of

coherent light. We have been discussing

Page 14: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

14

Can also get two coherent rays from thin films.

Page 15: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

15

Page 16: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

16

We will discuss the interference between rays

coming from the two surfaces on opposite sides of

a space filled with liquid (thin film) or air.

First: we need to know that when light reflects

from a surface sometimes it undergoes a phase

shift of 1800.

For example if a ray is in air 4� = 1.005and reflects

at the surface with water 4� = 1.335back into the

air it does not undergo a phase shift.

But if a ray is in glass 4� = 1.335and reflects at the

surface with air 4� = 1.005 back into the glass it

undergoes a 1800 phase shift.

Page 17: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

17

Rule

If ray goes from low n material and reflects at

surface of high n material no phase shift.

If ray goes from high n material and reflects at

surface with low n material 180 degree phase

shift.

6%�7 89:;9</9=:8>1?@@@@@@@@@@@A�B��# �B > �7

No phase shift.

But

6%�B 89:;9</9=:8>1?@@@@@@@@@@@A�7��# �B > �7

1800

(half wavelength) phase shift

Page 18: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

18

Now consider we have a film as shown

Assume perpendicular.

Film thickness where shown �.

Page 19: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

19

No phase shift at either surface or phase shift at

both surfaces

Constructive interference if

2� = ��� = 0, 1, 2, 3, …

But if one surface has phase shift and other does

not

Destructive interference.

Or

No phase shift at either surface or phase shift at

both surfaces

Destructive interference if

2� = �� +��! �� = 0, 1, 2, 3, …

Page 20: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

20

Example 26.3

Find separation of interference fringes.

One reflection (top) – no phase shift other

(bottom) – phase shift.

Glass

Air

Page 21: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

21

Equation for destructive interference

2� = ��� = 0, 1, 2, 3, …

Where glass touches – destructive interference.

From figure

�D =

ℎ�

So

� = Dℎ�

Therefore

2 EDℎ� F = ��

D = � E �2ℎF � = ���2ℎ

Page 22: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

22

D = � G40.1�54500D10IJ�5240.02D10IK�5 L

D = �41.25��5

Page 23: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

23

EXAMPLES OF INTERFERENCE PHENOMONO

Newton’s Rings

Page 24: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

24

Page 25: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

25

Nonreflective Coatings

Page 26: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

26

DIFFRACTION

Light goes in straight line.

Therefore would expect sharp shadow of object on

a screen.

But

Page 27: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

27

Consider light going through single slit.

This shows a ray from the top of the slit and one

from half way down the slit (middle).

Or looking only at the slit

Page 28: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

28

The difference in path distance to the screen is

"��ℎM$%%. = �2 sin '

If the path difference is one half wave length –

destructive interference.

Therefore the requirement for a dark fringe is

�2 sin ' = ±

�2

sin ' = ± ��

Page 29: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

29

If you divide the slit into 4 regions

If the path difference is one half wave length –

destructive interference.

Therefore the requirement for a dark fringe is

�4 sin ' = ±

�2

sin ' = ±2 ��

Becomes a/4

Becomes O/Q sinθ

Page 30: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

30

Divide the slit into more sections and can show

The requirements for dark fringes are

sin ' = � ��4� = ±1,±2,±3,… 5

Page 31: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

31

If the wavelength of light is much smaller than the

slit width (and normally it is) then

��� ≪ 14���(&����5

Therefore

' ≪ 14���(&����5

And

sin ' ≈ '

Therefore for dark fringes

' ≈ ��� 4� = ±1,±2,±3,… 5

Page 32: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

32

Also for

Use for distance to screen ) = D

Then tan ' = ST

And for the ��ℎ dark band

tan '1 =(1)

Page 33: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

33

If the screen is a distance from the slit such that

) ≫ (1

And it normally is

Then ' ≪ 14���(&����5

And tan '1 ≈'1

Therefore

'1 ≈(1)

Page 34: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

34

Then using

' ≈ ��� 4� = ±1,±2,±3,… 5

'1 ≈(1) ≈ ��� 4� = ±1,±2,±3,… 5

Solve for (1

(1 ≈ )��� 4� = ±1, ± 3, ± 5,… 5

This is equation 26.10 in the book.

Page 35: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

35

Multiple Slits

Path difference will be # sin '

Page 36: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

36

Constructive interference occurs for

# sin ' = ��4� = 0, ±1,±2,±3,… . 5

More complicated than two slit diffraction

Page 37: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

37

Eight Slit

Page 38: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

38

More – 16 slits

Page 39: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

39

DIFFRACTION GRATINGS

Prisms refract light different amounts depending

on the wavelength of the light.

Note short wavelengths (blue) are refracted more

than he long wavelengths (red).

Page 40: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

40

Diffraction Gratings will do much the same.

Page 41: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

41

The equation for the maxima is the same as for

multiple slits.

# sin ' = ��4� = 0, ±1,±2,±3,… . 5

Note

sin ' = ��#

Thus long wavelengths diffracted more than short

wavelengths. (Opposite to prisim.)

Page 42: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

42

X-RAY DIFFRACTION

First experiments in 1912.

Page 43: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

43

Crystal is uniform arrangement of atoms forming

planes for diffraction.

Page 44: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

44

Gives pattern

Page 45: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

45

Consider the atoms as all lined up on the sites and

represented by the dots shown.

Page 46: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

46

Look at top row for example

Path lengths are equal when 'B ='8

Page 47: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

47

Therefore when the two angles are equal get

constructive interference from diffraction from

rows.

Then considering two rows one beneath the other.

Page 48: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

48

Additional constructive interference when path

lengths are equal to integer times wavelength of

x-rays.

2#&$�' = ��4� = 1, 2, 3, … . . 5

When both conditions are satisfied

1. 'B ='8

And

2. 2#&$�' = ��

When these conditions are not satisfied radiation

interferes destructively.

Therefore obtain diffraction pattern characteristic

of crystal.

Page 49: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

49

Scattering and thus diffraction can occur from

various planes within the crystal.

Page 50: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

50

CIRCULAR APERTURES

Light travelling through a small circular aperture is

diffracted also.

Page 51: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

51

The angular locations of the dark rings are given

by:

sin '� = 1.22 �M

sin '� = 2.23 �M

sin 'K = 3.24 �M

OBSERVING OBJECTS THROUGH VARIOUS SIZE

APERTURES.

Page 52: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

52

Page 53: CHAPTER 26 INTERFERENCE - Texas A&M Universitypeople.physics.tamu.edu/adair/phys202/CHAPTER 26 INTERFERENCE.pdfchapter 26 interference and diffraction interference constructive destructive

53

If the aperture in (a) were smaller 3 and 4 would

appear as one object.

The larger the aperture the better the resolving

power.

Lord Rayleigh proposed a criterion for telescopes

(and other optical instruments) to give a measure

for their capability.

Two objects can only be resolved if the center of

the second just falls at a distance of the center of

the first dark ring of the first.

The limit of resolution, '89U for a telescope (or

other optical instrument):

'89U = 1.22 �M