Tài liệu Quantum Physics doc

A remarkable phenomen takes place, if two sources satisfy some Two sources have the same frequency f the same wave length  Two souces are permanently in phase, or , at least, have any

GENERAL PHYSICS III

Optics

&

Quantum Physics

What does we learn in Gen Phys III?

Many physical phenomena of great practical interest to engineers, chemists, biologists, physicists, etc were not in Gen Phys I & II

 Wave phenomena of light:

 Interference: what happens when two or more waves overlap?

(Light passing through two slits give such kind of picture)

Interference!

 Quantum Physics:

The development of experimental equiment and techniques  modern physics can go inside the microscopic world (atoms, electrons, nucleus, etc.)

 New principles, new laws for the microscopic (subatomic) world were discoverved

• Diffraction: The image of an object is not

exact in fine details.

For example, the image of a circular disk is diffused

Interference & diffraction can be analyzed if we regard light as a wave

 The basis concept: wave  particle duality

Examples: light wave  photon

electron  electron wave etc…

• Subatomic objects obey new mechanics: quantum mechanics

On the basis of quatum mechanics we study structure and properties of atoms, nucleus, solids, laser rays, etc…

Chapter XVII Interference of light

§ 1 Interference of coherent sources of light

§ 2 Interference in thin films

§ 3 Interferometer

§1 Interference of light from coherent sources:

We consider an overlap of light that comes from two sources

A remarkable phenomen takes place, if two sources satisfy some

Two sources have the same frequency f (the same wave length )

Two souces are permanently in phase, or , at least, have any definiteconstant phase difference

Then, two sources are called coherent sources.

1.1 Coherent sources of light:

Recall the formula for a sinusoidal e-m wave:

2wavelength wavenumber or wavevectorfrequency 2 angular frequency

→ However one can produce approximately monochromatic light:

• by using filters which block all but a very narrow range

of wave length

• by using light from a laser

1.2 Interference of light through narrow slits:

Monochromatic

light source at a

great distance,

or a laser. Slit pattern Observation screen

Young’s experiment on double-slit interference

(Thomas Young performed in 1800)

Light (wavelength is incident on a two-slit (two narrow,

rectangular openings) apparatus:

 If either one of the slits is closed, a

diffuse image of the other slit will appear

on the screen (The image will be

“diffuse” due to diffraction We will

discuss this effect in more detail

later.)

Monochromatic light (wavelength )

S 1

S 2

screen

Diffraction profile

I 1

 If both slits are now open, we see

interference “fringes” (light and dark

bands), corresponding to constructive

and destructive interference of the

electric-field amplitudes from both

Important quantity: path difference  = r 2 - r 1

The light density at the location of observer depends on the

A path difference corresponds to a phase difference of

two waves at the observer’s point

 One has a simple formula for the path difference, ,

when the observer is far from sources

(Assume 2 sources radiating in phase)



The corresponding phase difference

at the observer’s point:

= dsin= m Constructive Interference

= dsin= (m + 1 / 2 ) Destructive Interference

m=0 m=1 m=2

m=-1 m=-2

-/d

r

Usually we care about the linear

(as opposed to angular)

displacement y of the pattern (because our screens are often flat):

are in phase and reinforce each other, we say

that there is constructive interference

at these points

If m + 1)→ two waves

cancell each other → there is

destructive interference

L

The slit-spacing d is often large compared to ,so that is small

Then we can use the small angle approximations to simplify our results:

y = L tan L (in radians)

For small angles: (<< 1 radian)

sin tan (only in radians!)

1 What is the spacing y between fringe maxima on a screen 2m away?

2 If we increase the spacing between the slits, what will happen to y?

a decrease b stay the same c increase

3 If we instead use a green laser (smaller ), y will?

a decrease b stay the same c increase

1 What is the spacing y between fringe maxima on a screen 2m away?

2 If we increase the spacing between the slits, what will happen to y?

a decrease b stay the same c increase

3 If we instead use a green laser (smaller ), y will?

a decrease b stay the same c increase

1 What is the spacing y between fringe maxima on a screen 2m away?

2 If we increase the spacing between the slits, what will happen to y?

a decrease b stay the same c increase

3 If we instead use a green laser (smaller ), y will?

a decrease b stay the same c increase

 Note:

If a monochromatic source is replaced by a white light one →

how is the interference picture?

We have known that the location of (light or dark) fringers depends

on the wavelength therfore

• At y = 0 (the center light fringer) the maxima for all wavelengthscoincide → there is a white light fringer

• The nearby fringers have spectrum colors (like in rainbow)

• Far fringers are not visible (are diffused)

§2 Interference in thin films:

This kind of interference takes place when light reflects from athin film (for example, a soap bubble, a thin layer of oil floating

on water)

In this case there is an overlap

of light waves: one is reflected

from the upper, the other from

the lower surface

2.1 Calculation of path difference of two light waves:

First we consider the case that the incident light is monochromaticwith the wavelength 

eye

b: the thickness of the film

n: the index of refraction

the path difference between

the reflected waves 1 & 2

By elementary geometry it is

not difficult to obtain

Using the formula one can eliminate i 1 or i 2

We must take into account one more effect: the phase shift of

a wave after reflection

The path difference of two reflected waves depends on b, i 1 (or i 2)

At the points that satisfy m (m = 0, ±1, ±2, ) → we havecnstructive interference

At the points that satisfy = (m+1/2)→ destructive interference

We use the follwing theoretical results from Maxwell’s theory of

electromagetism:

• If na > nb → the phase shift of

reflected wave relative to the incident

wave is zero

• If na < nb → the phase shift of

reflected wave relative to the incident

wave is radian ( a half cycle)

na

nb

We can take into account this phase shift by introducing a

complementary term in the formula of path difference 

2.2 Interference on a film with two parallel surfaces:

Recall the formula

there will be constructive or destructive interference that depends

on incident angles i1 → the interference picture will be light & darkrings centered at O It’s called interference rings with the same

inclination

2.3 Interference on a thin wedge:

→ There is interference between

two light rays 1 & 2, reflected

from the upper & the lower

sides, at the points of thickness b

Shine a beam of parallel light

rays on a thin wedge

Interference takes place also for

light reflected at other points, for example, between the rays 1’ & 2’

With small angles we can use the previous formula for the pathdifference 

There will be constructive or destructive interference that depends

on the thickness b at reflected points On the screen we have light &dark interference fringers These are called interference fringerswith the same thickness

lens

• Using a glass plate and a lens

one can create an air wedge

between them

• The incident light is normal to the flat

plane of the lens One can observe the

interference of light waves reflected

from the air wedge

•The interference picture is a system of

light & dark rings

 Notes:

Interference fringers with the same inclination are observed

under the conditions: b = const; incident angles i vary.

Interference fringers with the same thickness are observed

under the conditions: i = const (parallel beam); b varies.

If the light is white → the fringers have rainbow colors

Under real conditions, when you observe a soap bubble or a thinlayer of oil floating on water, you see bands of color → these areinterference fringers mixing of both types (incident angles &

thickness of films can both vary

Interference on thin film has many application in engineering,for example, to check the quality of processing surfaces of

material

Beam splitter

Monochromatic

source

Compensator plate

• Beam splitter P 1: A glass plate

with a thin coating of silver

→ Light can reflect on and

pass through it

• Compensator plate P 2 : A plate identical to P1, but without silver layer.

It’s role is to ensure that rays 1 &2 pass through the same path insideglass (by 3 times of thickness of one plate)

Observer

Interference picture depends on path difference between two

rays 1’ & 2’ (it equals the difference of the paths P1-M1-P1 and

Then M1 M2’ / 500.000, it means that by measuring M1 M2’ one

can have precisely the result for 

We have known about the Michelson-Morley experiment that proved

the invariance of light speed c, one of principles of theory of relativity.

Conditions for interference: Light waves are from coherent sources.Practically, the best way to have coherent sources is to split lightwaves from a unique monochromatic source, then direct them to

overlap

Vibration state of each invidual wave at any point depends on opticalpath length n.L, where L is geometrical length → the important

quantity for interference is optical path difference of two waves:

* If = m → the phase difference m()

→ two light waves are in phase, and reinforce each other

→ constructive interference

* If = (m + ½) (→ the phase difference = (2m+1) 

→ two light waves have opposite phases, and cancell each other

→ destructive interference

The path length difference between two light rays reflected fromthe upper and the lower surfaces of a thin plate is

* In the condition that b = const; i1 varies → interference

fringers are called fringers with the same inclination

* In the condition that i 1 = const; b varies → interference

fringers are called fringers with the same thickness

This formula can applied to two cases: