Fundamental Physics II PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES Vungtau, 2013 Pham...

Fundamental Physics II

PETROVIETNAM UNIVERSITYFACULTY OF FUNDAMENTAL SCIENCES

Vungtau, 2013

Pham Hong QuangE-mail: [email protected]

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Chapter 7

Pham Hong Quang Fundamental of Drilling and Production

Diffraction

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7.1 Diffraction is a wave effect


In his 1704 treatise on the theory of optical phenomena (Opticks), Sir Isaac Newton wrote that "light is never known to follow crooked passages nor to bend into the shadow".

He explained this observation by describing how particles of light always travel in straight lines, and how objects positioned within the path of light particles would cast a shadow because the particles could not spread out behind the object.

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On a much smaller scale, when light waves pass near a barrier, they tend to bend around that barrier and spread at an angles.

This phenomenon is known as diffraction of the light, and occurs when a light wave passes very close to the edge of an object or through a tiny opening, such as a slit or aperture.

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Diffraction is a wave effect

Interference pattern of light and dark bands around the edge of the object.

Diffraction is often explained in terms of the Huygens principle, which states that each point on a wavefront can be considered as a source of a new wave.

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All points on a wavefront serve as point sources of spherical secondary wavelets. After a time t, the new position of the wavefront will be that of a surface tangent to these secondary wavefronts

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Using Fresnel's theory, a bright spot should appear behind a circular obstruction,

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7.2 Diffraction by a Single Slit


D >> a, rays are parallel

Divide the screen into two zones of width a/2

Find the first minima above the midpoint by pairing up rays from the top point of the top zone and the top point of the bottom zone

Rays are in phase at the slit but must be out of phase by by λ/2 at screen

The path length difference = a/2 sin θ

Locate the First Minima

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Repeat for other pairs of rays in the upper zone and lower zone: the first dark fringe occurs when:

a/2 sin θ = λ/2

a sinθ =λ first minima

If we narrow the slit the angle must get biggerwhat happens when a = λ?

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Repeat the process for paired rays (4) from corresponding points from each of the zonesRays are in phase at the slit but must be out of phase by by λ/2 at screen

Subsequent Minima

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Intensity in Single-Slit Diffraction PatternLight passing

through a single slit can be divided into a series of narrower strips; each contributes the same amplitude to the total intensity on the screen, but the phases differ due to the differing path lengths:

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Slit of width D divided into N strips of width Δy. Each strip is a wave with intensity of I0/N. Path difference between two adjacent strips is and the corresponding phase angle difference is . The intensity of the diffraction is, by superposition, the vector sum of the N strips of light with N approaching infinity.

sinyN

ntN

EE

N

nN

sinlim1

0

0

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Phasor diagrams give us the intensity as a function of angle.

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Finally, we have the phase difference and the intensity as a function of angle:

.

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7.3 Diffraction in the Double-Slit Experiment


Diffraction plus interference

I() Im cos2() sin2 2

d sin

dsin=m m =0,1,2.. maxima

asin

asin = m m =1,2,3.. minima

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7.3 Diffraction in the Double-Slit Experiment


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7.4 Diffraction Gratings


Like the double slit arrangement but with a much greater number of slits (rulings), sometimes as many as several 1000 per millimeter

Light passed through the grating forms narrow interference fringes that can be analyzed to determine the wavelength

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Here is the diffraction pattern for five slits:

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Position of maxima, where all waves interfere constructively are found with a familiar procedure:

So the angle to a particular line depends on the wavelength being used

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Dispersion

In order to distinguish different wavelengths that are close to each other a diffraction grating must spread out the lines associated with each wavelength. Dispersion is the term used to quantify this and is defined as

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Δθ is the angular separation between two lines that differ by Δλ. The larger D the larger the angular separation between lines of different λ.

It can be shown that

and D gets larger for higher order (m) and smaller grating spacing (d)

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Resolving Power

To make lines that whose wavelengths are close together (to resolve them) the line should be as narrow as possible

The resolving power is defined by

where λavg is the average of the two wavelengths studied and Δλ is the difference between them. Large R allows two close emission lines to be resolved. It can be shown that

To get a high resolving power we should use as many rulings

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Three gratings illuminated with light of λ=589 nm, m = 1

Grating N d(nm) θ D(o/μm) R

A 10000 2540 13.4 23.2 10000

B 20000 2540 13.4 23.2 20000

C 10000 1360 25.5 46.3 10000

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7.5 Limits of Resolution; Circular Apertures


Resolution is the distance at which a lens can barely distinguish two separate objects.

Resolution is limited by aberrations and by diffraction. Aberrations can be minimized, but diffraction is unavoidable; it is due to the size of the lens compared to the wavelength of the light.

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For a circular aperture of diameter D, the central maximum has an angular width:

radians.in ,22.1 D

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The Rayleigh criterion states that two images are just resolvable when the center of one peak is over the first minimum of the other.

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On the left, there appears to be a single source; on the right, two sources can be clearly resolved.

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7.6 X-Ray Diffraction


Spacing between atomic layers in a crystal is the right size for diffracting X-rays; this is now used to determine crystal structure

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Bragg’s law, θ is Bragg’s angle

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36 -14 51 (*) - Zin c ite , s y n - Zn O - Y: 26 .37 % - d x by : 1 .0 00 - WL : 1 .5 40 56File : Qu an g-NDT-Zn O-Q6 .raw - Ty pe : 2Th a lo ne - Sta rt: 10 .00 0 ° - End : 7 0 .0 00 ° - Ste p : 0 .020 ° - Ste p time : 1 .0 s - Te mp.: 2 5 .0 °C (Roo m) - Anod e : Cu - Crea tion : 08 /09 /11 17 :11 :11

Lin (

Cps)

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

11 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

1 8 0

1 9 0

2 0 0

2 1 0

2 2 0

2 3 0

2 4 0

2 5 0

2-Thet a - Scale

1 0 2 0 3 0 4 0 5 0 6 0 7 0

d=

2.5

99

7

d=

2.4

73

0

d=

1.9

10

2

d=

1.4

76

1

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40Pham hong Quang 40 PetroVietnam Universityg

Thank you!

Fundamental Physics II PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES Vungtau, 2013 Pham...

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