fundamental physics ii petrovietnam university faculty of fundamental sciences vungtau, 2013 pham...
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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
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction is a wave effect
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction is a wave effect
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction is a wave effect
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction is a wave effect
Pham Hong Quang Fundamental of Drilling and Production
Using Fresnel's theory, a bright spot should appear behind a circular obstruction,
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7.2 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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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7.2 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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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7.2 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
Phasor diagrams give us the intensity as a function of angle.
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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
Finally, we have the phase difference and the intensity as a function of angle:
.
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7.2 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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7.1 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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7.2 Diffraction by a Single Slit
Pham Hong Quang Fundamental of Drilling and Production
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7.3 Diffraction in the Double-Slit Experiment
Pham Hong Quang Fundamental of Drilling and Production
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
Pham Hong Quang Fundamental of Drilling and Production
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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
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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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
Here is the diffraction pattern for five slits:
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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
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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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
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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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
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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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
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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7.4 Diffraction Gratings
Pham Hong Quang Fundamental of Drilling and Production
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
Pham Hong Quang Fundamental of Drilling and Production
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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7.5 Limits of Resolution; Circular Apertures
Pham Hong Quang Fundamental of Drilling and Production
For a circular aperture of diameter D, the central maximum has an angular width:
radians.in ,22.1 D
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7.5 Limits of Resolution; Circular Apertures
Pham Hong Quang Fundamental of Drilling and Production
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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7.5 Limits of Resolution; Circular Apertures
Pham Hong Quang Fundamental of Drilling and Production
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
Pham Hong Quang Fundamental of Drilling and Production
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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7.6 X-Ray Diffraction
Pham Hong Quang Fundamental of Drilling and Production
Bragg’s law, θ is Bragg’s angle
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7.6 X-Ray Diffraction
Pham Hong Quang Fundamental of Drilling and Production
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7.6 X-Ray Diffraction
Pham Hong Quang Fundamental of Drilling and Production
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7.6 X-Ray Diffraction
Pham Hong Quang Fundamental of Drilling and Production
VNU-HN-SIEMENS D5005 - Mau ZnO - Q6
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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7.6 X-Ray Diffraction
Pham Hong Quang Fundamental of Drilling and Production
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40Pham hong Quang 40 PetroVietnam Universityg
Thank you!