Download Diffraction - ICT for IST

ICT for Innovative Science Teachers
Leonardo da Vinci programme
2009-1-PL1- LEO05- 05046
Diffraction
Diffraction effects may be
fascinating and provide useful
information, but they can also be
distracting and affect the quality
of images.
In this photograph, taken with
a reflecting telescope, diffraction
effects are present due the ‘spider’
arms supporting the secondary mirror.
CC 2011 ICT for IST
This project has been funded with support from the European Commission under the Lifelong
Learning Programme. This publication reflects the views only of the author, and the Commission
cannot be held responsible for any use which may be made of the information contained therein.
A. Introduction
The theme of this module is the phenomenon of diffraction, a fundamental
property of all types of wave motion, be they sound waves, water waves, or
electromagnetic waves such as visible light, x-rays and radio waves. The
activities exploit the use of ICT to help visualise some of the more abstract
aspects of diffraction and facilitate understanding of the mathematical
description of diffraction phenomena. There are three types of activities:
1. Video recording: Laboratory experiments with a ripple tank recorded
in a video format facilitating observations and analysis of plane and
circular water waves. The results permit investigation of the
relationships between wavelength and the dimensions of obstacles and
slits.
2. Simulation: Visual aids, including a simulated ripple tank, to facilitate
virtual experiments with diffracted waves. The results are used to
investigate the relationships between wavelength and experimental
parameters.
3. Remote experiments: Data-logging experiments on single slit
diffraction with laser light, conducted via an Internet connection to
apparatus in a remotely located laboratory. The measurements
obtained are used to calculate the wavelength of the laser light.
1. Background theory
1. INTRODUCTION
Diffraction refers to various phenomena which occur when a wave encounters
an obstacle. Diffraction occurs with all waves, including sound waves, water
waves, and electromagnetic waves such as visible light, x-rays and radio waves.
Reduction to 2-dimensional problem
The simplest descriptions of diffraction are those in which the situation can be
reduced to a two-dimensional problem. For water waves, this is already the
case, water waves propagate only on the surface of the water. That is why the
basic introduction to the diffraction phenomena can be taught using the ripple
tank (water) and then through various simulations and models, available on the
Internet.
Diffraction effects - 2
Plane and circular waves
It seems quite effective to present these phenomena in a systematic way, using
at first planar and then later circular waves.
Dimension of slits/obstacles and wavelength
It also seems very effective to systematically present diffraction phenomena
using both obstacles and openings (slits) and to emphasize the important
relation between the size (dimension „u‟) of obstacles (or slits) and the
wavelength (lambda). Again the systematic way of presenting the situation
under different conditions helps to develop conceptual understanding:
1. Obstacle (or slit) is much smaller than the wavelength (u<<lambda),
2. Obstacle (or slit) is much larger than the wavelength (u>>lambda),
3. Obstacle (or slit) is similar in size to the wave length (u ≈ lambda)
Presenting all these cases, for both planar and circular waves and for both
obstacles and slits (altogether 12 cases), requires good experimental skills and a
large database of videos, simulation files or, at the least, photos). In the
following, you can find all the above illustrations and examples, ordered in a
tables, offering for each specific case files with simulations, photos and videos or
links to files, which are non-downloadable or protected by copyright. These
comprise a large number of examples and a non-systematic (chaotic) way of
picking up and presenting just a few of them, which illustrate a phenomenon but
not the principles, should be avoided.
It seems also very useful, especially for smaller children, or those, who hear
about these phenomena for the first time in their life, to start with the water
waves, continue with the sound and finally to present effects with light.
After basic systematic demonstration of the diffraction phenomena, it is possible
to motivate students with the demonstration of the phenomenon with two or
more slits, gratings, three dimensional cases, examples from the technical world
and from the nature, etc... just as a nice physics show and illustration of basic
principles.
Diffraction effects - 3
2. BASIC TERMS
Here are the basic terms we will meet in this module:
Plane wave
Fig. 1. Illustration – plane wave on a ripple tank – projection (a) and detail(b)
Circular wave
Fig. 2. Illustration – circle wave in the ripple tank – projection (a) and detail(b)
Both circular and plane waves may be illustrated using the following
recommended video files or simulation (tables 1-4). They are all accessible on
http://www.acoustics.salford.ac.uk/feschools/waves/dripvideo2.htm
Let‟s discuss with students the following special cases. Ask them to notice the
waves in geometric shadow.
Diffraction effects - 4
Diffraction on a slit
1. Large slit (u>> lambda)
2. Narrow slit (u<< lambda)
Schematic illustration of the bending plane waves at very narrow slit: In this
case a slit could be considered as the point source wave, generating, according
the Huygens principle, a circle wave in all directions with equal intensity.
3. Slit width is comparable with the wavelength (lambda ≈ u)
Schematic illustration of the diffraction of a plane wave at a single slit which
width is comparable to the wavelength of waves: In this case there is an
interference of elementary waves, which results in the waves spreading not only
straight ahead, but also to the sides. The intensity of waves in this case depends
on the direction at which a wave spreads; a pattern of maxima and minima as
seen to emerge. Greatest strength lies in the direction of propagation of waves.
Diffraction effects - 5
The other maxima are lower intensity. A similar phenomenon can be observed in
the bending of light at a slit in optics, and also in acoustics.
Diffraction on one single obstacle
After explaining the single slit, we can use computer-based simulations for
illustrating similar effects – diffraction by an obstacle. In thus (very simple) way,
we can help children to understand, why they can hear somebody around the
corner, but not to see him.
Fig. 3. Diffraction by a single obstacle – simulation of a ripple tank (right)
http://www.acoustics.salford.ac.uk/feschools/waves/diffract.htm#object
Bending the waves around the corner (left)
http://www.phy.hk/wiki/englishhtm/Diffraction3.htm
After explaining sound and water waves, we can talk a bit about light waves.
3. HISTORICAL REMARKS AND EXPLANATION OF TITLES AND NAMES
Although diffraction had been observed by many scientists and ordinary people,
the bending of light was first well described around 1660 by an Italian teacher of
mathematics - Francesco Maria Grimaldi.
Francesco Maria Grimaldi
Grimaldi let the sunlight fall into a darkened room through a small round hole.
Then he held various subjects in the path of the light and studied the properties
of their shadow. He first found that the shadows are blurred, and in addition,
bounded by coloured stripes.
Augustin Jean Fresnel and Joseph von Fraunhofer
Thanks to a long history of observing diffraction patterns with light, we have
many historical experiments and names, connected with them.
The best known are Augustin Jean Fresnel and Joseph von Fraunhofer. Both set
up experiments and observed the diffraction patterns which occur. Their
experimental settings were different and thus they supposed also that the
Diffraction effects - 6
observed phenomena are different. Later, their colleagues named the observed
phenomena after them.
Important Note: In principal, we can observe both Fresnel and Fraunhofer diffraction
under the same experimental settings, but in a traditional (historical) laboratory
conditions it was hard to reach.
We can illustrate the historical way of classifying these phenomena, in a
simplified but sufficient for secondary school student‟s explanation.
Fresnel diffraction
We can say that the Fresnel diffraction phenomena occur when there is a
spherical wave, meeting the obstacle or slit. Thus the diffraction phenomena at
small distances from the (point) light source with sufficient precision can be
considered as Fresnel diffraction phenomena.
Fraunhofer diffraction
Fraunhofer diffraction phenomena occur when there is a plane wave. Thus
diffraction phenomena at large distances from the (point) source with sufficient
precision can be considered as Fraunhofer‟s diffraction phenomena.
Diffraction due to a single slit, the case of plane wave (laser, day light, light from
the source point, which is in the “infinite” distance (very very far) from the point
source wave) can be illustrated with the following examples.
Understanding the term “spherical” or “planar” must be also done in relation to
the dimension of the slit or obstacle. For very very narrow slits, almost all waves
might be “planar”. The following picture illustrate the transition from so called
Fresnel„s to so called Fraunhofer„s diffraction.
Fig. 4. From Fresnel„s to Fraunhofer„s diffraction (decreasing width of the slit)
Diffraction effects - 7
2. Pre-requisite knowledge required
1.
2.
3.
4.
Plane wave
Spherical wave
Huygens' principle
Reflection, refraction – possibilities for illustration of the phenomena and
repetition of the basic facts – e.g.:
a. laser
b. Interference - interference of waves (can be illustrated by the following
applet - http://phet.colorado.edu/en/simulation/wave-interference, or by
a real experiments in a ripple tank)
B Didactical approach
.
1. Pedagogical context
Emphasis on the diversity of
phenomena, understanding
differences among
interference x diffraction x
scattering
Emphasis on analogies - the
mechanical wave (dripping
water, ripple tank), acoustic
waves, electromagnetic
waves (X rays, etc.) and
observation of optical
phenomena
Emphasis on immediate
feedback, practical
experience and practical
applications
Emphasis on a systematic
approach
2. Common student difficulties
Conceptual confusion between the phenomena of interference (superposition)
and diffraction (spreading)
Conceptual confusion between the phenomena of diffraction (spreading) and
refraction (bending)
Conceptual confusion between scattering and diffraction
Misinterpretation of this complex natural phenomenon, which is usually
observed together with many other different effects (interference, diffraction,
scattering), inappropriate simplification
Diffraction effects - 8
3. Evaluation of ICT
This section considers some of the practical arrangements for exploiting the use
of ICT to best effect, and discusses the qualities of the ICT methods which make
a special contribution to students‟ learning.
VIDEO RESOURCES AND SIMULATIONS
Diffraction of a plane wave on an obstacle
The following table cells contain the names of files, available on your CD, which
illustrate the phenomenon. For example, Fresnel_Fraunhofer.jar is a simulation
file which may be used as an illustration of the diffraction phenomenon when a
plane wave meets a large obstacle, as well as for illustrating the diffraction at a
very narrow obstacle, or at an obstacle whose dimension (u) is comparable with
the wavelength used.
large obstacle
u>> lambda
very narrow
obstacle
u<< lambda
obstacle
comparable
with the wave
length
u ≈ lambda
Plane
wave
simulationfiles
Fresnel_Fraunhofer
.jar
Fresnel_Fraunhofer.jar
Fresnel_Fraunhofer.j
ar
simulationslinks
http://www.phy.hk
/wiki/englishhtm/D
iffraction2.htm
http://www.phy.hk/wiki
/englishhtm/Diffraction
2.htm
http://www.phy.hk/w
iki/englishhtm/Diffrac
tion2.htm
video
plane_obstacle_lar
ge.wmv
plane_obstacle_narrow.
wmv
plane_obstacle_comp
arable.wmv
Table 1. Resources for diffraction of a plane wave meeting an obstacle
Diffraction of a circular wave on an obstacle
The table cells contain the names of files, available on your CD, which illustrate
the diffraction of a circular wave on an obstacle of different width. E.g.
“soundwaterlight- en.jar” or “diffraction_Fresnel_obstacle_slit.zip” are simulation
files, available to use for an illustration of the diffraction phenomenon when a
circular wave (of all kinds -mechanical –water, acoustical –sound or optical –
light) meets a large obstacle, as well as for illustrating the diffraction at a very
narrow obstacle, or at an obstacle whose dimension (u) is comparable with the
wavelength used. The last named file “diffraction_Fresnel_obstacle_slit.zip” also
illustrates diffraction phenomena with a slit.
Diffraction effects - 9
large obstacle
u>> lambda
very narrow
obstacle
u<< lambda
obstacle
comparable
with the wave
length
u≈ lambda
Circular
wave
simulationfiles
soundwaterlighten.jar
diffraction_Fresnel
_obstacle_slit
simulations
-links
http://phet.colorad
o.edu/en/simulatio
n/waveinterference
or
http://www.falstad
.com/diffraction/
soundwaterlight-en.jar
diffraction_Fresnel_obst
acle_slit
soundwaterlighten.jar
diffraction_Fresnel_o
bstacle_slit
http://phet.colorado.ed
u/en/simulation/waveinterference
http://phet.colorado.
edu/en/simulation/w
ave-interference
or
http://www.falstad.com
/diffraction/
or
http://www.falstad.c
om/diffraction/
Table 2. Resources for diffraction of a circular wave on an obstacle
Diffraction of a plane wave on a slit
The table cells contain the names of files, available on your CD, which illustrate
the diffraction of a plane wave on a slit of different width.
large slit
very narrow slit
u>> lambda
u<< lambda
slit comparable
with the wave
length
u≈ lambda
Plane
wave
photos files
plane_slit_large.jp
g
plane_slit_narrow.jpg
plane_slit_comparabl
e.jpg
simulationsfiles
Fresnel_Fraunhofer
.jar
Fresnel_Fraunhofer.jar
Fresnel_Fraunhofer.j
ar
simulationslinks
http://www.phy.hk
/wiki/englishhtm/D
iffraction.htm
http://www.phy.hk/wiki
/englishhtm/Diffraction.
htm
http://www.phy.hk/w
iki/englishhtm/Diffrac
tion.htm
Video files
plane_slit_large.w
mv
plane_slit_narrow.wmv
plane_slit_comparabl
e.wmv
Table 3. Resources for diffraction of a plane wave on a single slit
Diffraction effects - 10
Diffraction of a circular wave on a slit
The table cells contain the names of files, available on your CD, which illustrate
the diffraction of a circular wave on a slit of different width.
large slit
very narrow slit
u>> lambda
u<< lambda
slit comparable
with the wave
length
u≈ lambda
Circular
wave
photos –
files
circle_slit_large.jpg
circle_slit_narrow.jpg
circle_slit_comparabl
e.jpg
simulations
- files
soundwaterlightinterference_en.jar
soundwaterlightinterference_en.jar
soundwaterlightinterference_en.jar
diffraction_Fresnel
_obstacle_slit
diffraction_Fresnel_obst
acle_slit
diffraction_Fresnel_o
bstacle_slit
http://phet.colorad
o.edu/en/simulatio
n/waveinterference
http://phet.colorado.ed
u/en/simulation/waveinterference
http://phet.colorado.
edu/en/simulation/w
ave-interference
or
http://www.falstad.com
/diffraction/
or
http://www.falstad.c
om/diffraction/
circle_slit_narrow.wmv
circle_slit_comparabl
e.wmv
simulationslinks
or
http://www.falstad
.com/diffraction/
video
circle_slit_large.w
mv
Table 4. Resources for diffraction of a circular wave on a single slit
REMOTE AND VIRTUAL LABORATORIES
Diffraction on a single slit, the case of plane wave (laser, day light, light from the
source point, which is in the “infinite” distance (very very far) from the point
source wave) is possible to illustrate using following:
1. Numerical model of diffraction pattern from a slit of width four wavelengths
with an incident plane wave. We can easily observe the main central beam,
minima and maxima. Adopted from
http://sirrah.troja.mff.cuni.cz/~mira/famdifr/famdifr.html)
Diffraction effects - 11
Fig. 5. Figure represents numerical model of diffraction pattern from a slit of
width four wavelengths with an incident plane wave
2. The real observation of the same diffraction patterns on the screen might look
like on the following picture.
Fig. 6. Real time observation of the diffraction phenomena, provided by web
camera (a). The intensity graph obtained automatically with the use of intensity
sensor. Both obtained from Remote laboratory http://kdt13.karlov.mff.cuni.cz/sterbina_en.html.
Note for teachers:
It seems much better to explain the diffraction phenomena (plane wave, single slit) as
was presented above – simulation of the “photon density” or light intensity followed by
the real experiment (or opposite order), then to combine “ripple tank water wave “
simulation with the intensity graph like it is presented for example on Wikipedia – see
the following:
Diffraction effects - 12
Note: Basic explanation of the diffraction phenomena (single slit, 2 and more
slits, grating, plane wave, circle wave and many other constellations) is available
on Wikipedia the free encyclopaedia and large variety of other websites.
It is also available on this remote laboratory website:
http://www.ises.info/index.php/en/laboratory/experiment/difraction-onmicroobjects/physicalBackground
3. Resources for Student Activities
Activity
1. Real and video
recorded
experiments –
mechanics – (ripple
tank, ripple tank
records)
Software
program
Any video player
Files available in Remote
laboratory module
Diffraction
plane_obstacle_large.wmv
plane_obstacle_narrow.wmv
plane_obstacle_comparable.wmv
circle_obstacle_large.wmv
plane_obstacle_narrow.wmv
circle_obstacle_comparable.wmv
plane_slit_large.wmv
plane_slit_narrow.wmv
plane_slit_comparable.wmv
circle_slit_large.wmv
circle_slit_narrow.wmv
circle_slit_comparable.wmv
Diffraction effects - 13
2. Virtual
experiments (the
virtual ripple tank
and other
simulations)
Java virtual
machine,
Web browser
Any commander
to unzip files
3. Real experiment –
optics (single slit,
plane wave) in
combination with
simulation of the
same phenomena
http://www.phy.hk/wiki/englishhtm/Diffrac
tion2.htm,
http://www.phy.hk/wiki/englishhtm/Diffrac
tion.htm
soundwaterlight-en.jar (use water)
http://phet.colorado.edu/en/simulation/wa
ve-interference (use water)
soundwaterlight-en.jar (use Light)
Java virtual
machine,
Web browser
4. Remote
laboratory
experiment (single
slit, plane wave) and
remote data logging
Remote
laboratory, IE
browser,
5. Remote
laboratory
experiment (single
slit, plane wave) and
data processing
(advanced students)
Remote
laboratory, IE
browser,
6. Application level –
“Play” with the
practical application
and the use of
diffraction
phenomena
(advanced students)
Any video player,
java virtual
machine
http://phet.colorado.edu/en/simulation/wa
ve-interference (use light)
http://www.phy.hk/wiki/englishhtm/Diffrac
tion.htm (slit)
Use the remote laboratory experiment
available on http://kdt13.karlov.mff.cuni.cz/sterbina_en.html
Web browser
Use the remote laboratory experiment
available on http://kdt13.karlov.mff.cuni.cz/sterbina_en.html
Web browser
MS Excel
http://www.falstad.com/diffraction/
http://chem.lapeer.org/PhysicsDocs/Goals
2000/Laser2.html
Crystallography_RHEED_setup.gif
Crystallography_Bragg_Diffraction.png
Crystallography_Lauegram_Si_100_4foldSymm_Inclined.png
Crystallography_Lauegram_4foldSymmetry.jpg
And many others (see the tables in Activity
6)
Diffraction effects - 14
C Student Activities
.
ACTIVITY 1. DIFFRACTION EXPERIMENTS WITH A
RIPPLE TANK USING VIDEO RECORDINGS
Learning Objectives:
1. To learn how to observe and analyse real diffraction experiments with the
ripple tank using video recordings
2. To find out the rules relating wavelength with experimental parameters
3. To create hypotheses
Activity method:
In this activity the students will analyze the real (recorded) diffraction effects
in following situations: plane wave-obstacle-wavelength smaller, plane waveobstacle-wavelength comparable, plane wave-obstacle-wavelength larger,
plane wave-slit-wavelength smaller, plane wave-slit-wavelength comparable,
plane wave-slit-wavelength larger, circle wave-obstacle-wavelength smaller,
circle wave-obstacle-wavelength comparable, circle wave-obstacle-wavelength
larger, circle wave-slit-wavelength smaller, circle wave-slit-wavelength
comparable, circle wave-slit-wavelength larger.
Students shall observe the real (or video) experiment and try to find out the
rules and relationships between the wavelength and the dimension of the
obstacle/slit
Teachers can use the resources recommended above in Tables 1, 2, 3 and 4 or
a real ripple tank (if available) to illustrate the basic terms and phenomena.
Hints and tips:
Ripple tank scheme and description for both teachers and students:
In a ripple tank the surface water waves are produced by a pulse of air, which
causes a metal bar to vibrate (older apparatus uses simple mechanical
vibrations). The waves so produced are observed using stroboscopic
illumination. By adjusting the frequency of the stroboscope, wave patterns
might appear to be stationary. This occurs when the frequency of rotation is
equal to or is a simple multiple of the frequency of the water waves.
Diffraction effects - 15
.
ACTIVITY 2. EXPERIMENTS WITH THE VIRTUAL
RIPPLE TANK AND OTHER SIMULATIONS
Learning Objectives:
1. To learn and understand the differences between real experiment (and real
data acquisition) and virtual experiment (simulations/models)
2. To understand the advantages and limits of virtual experiments
3. To understand that the virtual experiment is not a way to verify hypotheses
Activity method:
In this activity the students will analyze the simulated diffraction effects in the
set/subset of following situations: plane wave-obstacle-wavelength smaller,
plane wave-obstacle-wavelength comparable, plane wave-obstacle-wavelength
larger, plane wave-slit-wavelength smaller, plane wave-slit-wavelength
comparable, plane wave-slit-wavelength larger, circle wave-obstaclewavelength smaller, circle wave-obstacle-wavelength comparable, circle waveobstacle-wavelength larger, circle wave-slit-wavelength smaller, circle waveslit-wavelength comparable, circle wave-slit-wavelength larger.
Students shall compare the real behaviour, they observed in activity 1, to the
simulations of the same phenomena. They should understand, that the virtual
experiment (simulation) is NOT the real proof of hypotheses, created in
activity 1 and cannot be used for verification of hypotheses.
The teacher has to find out what appropriate guidance for useful investigations
and explorations of the students is required. We highly recommend him/her to
make a systematic progress, or, at least, to explain the system and regularity
within these phenomena.
Diffraction effects - 16
ACTIVITY 3. REAL OPTICS EXPERIMENTS WITH A
SINGLE SLIT COMBINED WITH A SIMULATION
Learning Objectives:
1. To develop experimental skills (real and virtual) in the study of optics
2. To find out the analogies between mechanical and optical phenomena
3. To understand the limits of both virtual and real experimenting
Activity method:
In this activity the students will analyze the diffraction effects in optics.
They will use different kinds of slits and different wavelengths - red/green/blue
lasers and white light.
Students themselves should suggest the experimental setup and to discover
the systematic way to reveal and to prove their hypotheses.
They again shall compare the real behaviour, they observed, to the
simulations of the same phenomena. They should understand that the virtual
experiment (simulation) is NOT the real proof of a hypothesis created in
activity 1 and cannot be used for verification of a hypothesis.
The teacher has to find out what appropriate guidance for useful investigations
and explorations of the students is required. We highly recommend him/her to
make a systematic progress, or, at least, to explain the basic laws and
regularities within this phenomenon.
Diffraction effects - 17
ACTIVITY 4. REMOTE LABORATORY EXPERIMENT
(SINGLE SLIT, PLANE WAVE) AND REMOTE DATA
LOGGING
Learning Objectives:
1. To perform a remote laboratory experiment
2. To understand the advantages and limits of remote experimenting and datalogging
Activity method:
Use the remote laboratory experiment available on http://kdt13.karlov.mff.cuni.cz/sterbina_en.html
Use the detailed description of tasks, which follows.
Notice: For routine incorporation onto the classroom activities or laboratory
work is necessary to limit the number of tasks, and offer logged data to
different groups without individual data-logging through the remote laboratory.
Performing the remote laboratory experiment:
All of the following tasks are based on remote laboratory at the Charles
University (http://kdt-13.karlov.mff.cuni.cz/sterbina_en.html). The ongoing
measurement can be simultaneously monitored by the web camera (left upper
corner).
1. First obtain some test measurements (for example, red laser, narrow slit).
Transfer the data to Excel, and display a chart. Compare the Excel chart to the
graph obtained directly from the web site. Explain and justify any difference you
found.
Tips for teachers:
Students notice the size discrepancy of the main and secondary peaks (maxima)
on the graph obtained directly from the remote laboratory. Ask students for the
reason.
Answer: The Y axis on a graph, generated automatically by the remote
laboratory is a logarithmic scale.
Diffraction effects - 18
Notice different distances between the secondary maxima.
Explanation: The scale on X axis of the graph, generated automatically by the
remote laboratory, is probably different then the scale you chose in your chart.
The final appearance depends on the values you choose (see the following
illustrations).
1 / Make first - experimental mea
2. Take measurements for the green laser and narrow slit. Note the significant
difference between what the eye sees (despite low-quality transmission of web
camera) and what appears on the graph.
Diffraction effects - 19
a) How many secondary maxima can be recognized by eye?
b) How many peaks you see on the graph? How many are you able to deduce
from the tables (data)? Explain the differences.
c) Why chart may look somewhat asymmetrically?
d) Why is primary maximum sometimes clipped?
Tips for teachers:
a) and b): The human eye is very sensitive sensor and can distinguish small
differences in the light intensity.
The sensor (phototransistor) is not so sensitive. For the majority of non human
sensors the intensity at for example 7th maximum is so low, that it fails.
c): The diffraction pattern, of course, is symmetric. There might be several
reasons for that pattern does not look as pretty as we would expect from text
books.
E.g.:
Green light maxima are very close to each other. The step of the sensor
(phototransistor) is relatively large and thus it may "miss" the real maximum /
minimum.
The intensity of light is outside of the range, measured by the sensor. Its
sensitivity could be reduced, but then we meet difficulties with distinguishing
secondary maxima. The result is then a graph that does not accurately capture
all the highs and also looks asymmetrically.
The sensor itself has non infinitesimal size (1-2 mm) and could, in case of very
close peaks summarize light intensity contributions.
Laser requires some time for the optimized work (about 1 min). Wait then after
each setup a minute or two and analyze again.
Diffraction effects - 20
ACTIVITY 5. REMOTE LABORATORY EXPERIMENT
(SINGLE SLIT, PLANE WAVE) AND DATA
PROCESSING (ADVANCED STUDENTS)
Learning Objectives:
1. To obtain necessary skill for remote experiments data acquisition
2. To improve skills for data processing and to process data individually
3. To compare results and to negotiate reasons in teams, to understand deeply
the observed phenomena
Activity method:
This activity is focused on advanced physics students.
Students shall setup the experiment, to transfer data and to carry out the
charts.
After that they shall answer the sophisticated questions verifying the real
understanding of the problem.
The teacher has to find out what appropriate guidance of the students is
required for useful investigations and explorations.
We highly recommend him/her to push the students to work in a systematic
way.
Performing the activity:
Do the remaining measurements for the two wavelengths (λ1 = 632 ± 10 nm)
and λ2 = (532 ± 10 nm), and both slit widths at a constant distance a = (2152
± 1) mm from the slit lamp.
Transfer data into a spreadsheet and create graphs. Plot the intensity in a
logarithmic scale, location within a range of 50 mm to 150 mm. Work carefully
and always wait for the laser to operational status.
Answer the following questions:
Diffraction effects - 21
a) Why are green secondary maxima closer together than in the red light?
b) Why are the secondary maxima obtained at a wider aperture closer together?
c)/ Why are secondary maxima obtained at a wider aperture higher intensity?
d) Calculate the width of both narrow and wide slits from the known formulae for
Fraunhofer diffraction. Estimate the positions of individual peaks from the tables
transferred to a spreadsheet (reading is more accurate).
This calculation (3d) and associated measurement should be classified as a
separate task (e.g. laboratory work). Use the following, known relations
,
where I is the intensity, b the slit width and
diffraction.
the angle under which we observe
For the minima of intensity the following relationship is valid, where k is an
integer.
sin( )
calculated from the geometric arrangement of experiment,
namely the distance from the known position of the shield and the distance of
the k-th minimum from the centre of bending shapes.
For the estimation of these values use the measured data rather than chart.
Diffraction effects - 22
4) What is the intensity in the main maximum?
Relative value of the intensity of the main maximum is 1, all others (secondary)
maxima intensity have a value of less than 1. Namely: the first app. 0.047, the
second 0.016, third 0.0083 etc.
5) Evaluate the work in the remote laboratory. What additional information you
need to be able to correctly interpret the results or process?
Tips for teachers: the location of lasers, the characteristics of sensors, location
sensors for both lasers (change of intensity in the vertical plane of the screen),
the units (necessary for correct reading of maxima distances), step of the
intensity sensor, or other.
Note: to study the necessary theory use optics books or devoted web pages – in
Czech e.g. http://kdt-13.karlov.mff.cuni.cz/ohyb.html,
http://physics.mff.cuni.cz/vyuka/zfp/txt_u303.pdf,
physics.mff.cuni.cz/vyuka/zfp/mereni_306.pdf, or E. Klier: Optics, textbook,
SPN, Prague 1978.
Diffraction effects - 23
ACTIVITY 6. THE PRACTICAL APPLICATION AND
THE USE OF DIFFRACTION PHENOMENA
(ADVANCED STUDENTS)
Learning Objectives:
1. To appreciate the field of technical applications of diffraction
2. To apply understanding to some specific simple situations
Activity method:
In this activity the students, under the teacher‟s guidance, will discover the
large application area of the diffraction phenomena.
The teachers have to find out the appropriate guidance through the following
application tables and to pick up the methods and areas, they understand (at
least partially).
Tasks:
EXERCISE: READING LAUEGRAMS
Read the commentary below, look at the lauegrams and compare them.
1. Crystallography_Lauegram_4-foldSymmetry.jpg
Lauegram illustrating a four-fold symmetry.
2. Crystallography_Lauegram_Si_100_4-foldSymm_Inclined.png
Lauegram of a silicon crystal (cubic lattice) in a direction 100 has a four-fold
symmetry - see the perpendicular lines in the lauegram. In this case the crystal is
inclined a bit with respect to the direction 100
3. Crystallography_Lauegram_Si_111_3-foldSymm.jpg
Lauegram of a silicon crystal (cubic lattice) in the direction 111 has a three-fold
symmetry (there are three brightest points in the lauegram - compare with the sixfold symmetry).
4. Crystallography_Lauegram_6-foldSymm.jpg
Lauegram illustrating a six-fold symmetry (there are six brightest points in the
lauegram - compare with the three-fold symmetry).
5. Crystallography_Debyegram_Powder.jpg
Debyegram of a powder form sample - dependence of the intensity of X-rays on the
Bragg angle (2 Theta). The Bragg angle is shown in the figure:
Crystallography_Bragg_Diffraction.png
Diffraction effects - 24
Performing the activity:
Branches
Methods, Equipment Example
usage
diffraction
picture
Astronomy, Optical
systems
Collimation
of optical
axes
Astronomical
telescopes
(usually
reflectors like
Cassegrain
systems, etc.)
Astronomy_Collimation_
Poor.jpg
High
resolution
spectral
analysis
Spectrometer,
spectrograph
(with
diffractive
gratings)
Astrophysics_Spectrum.
jpg
http://www.noao.edu/imag
e_gallery/images/d5/suny.j
pg
* e.g.
diffraction
on a piece
of hair to
determine
its diameter
Laser pointer,
source of laser
beam
Measurements_Hair.jpg
http://chem.lapeer.org/Phy
sicsDocs/Goals2000/Laser2.
html
Radiowaves
Anthenna /
Aerial
See Fig. 3
Storage of 3D images Holography
Hologram
Holography_Record.png http://en.wikipedia.org/wiki
Holography_Reconstruct /Holography
ion.png
Biophysics and
biochemistry
Protein
structure
research
Diffractometer
Biophysics_Diffractogra
m_Protein.jpg
Many
methods –
see the
following
table
Diffractometer
Astrophysics and
optics, Spectroscopy,
Infra-red
spectroscopy
Measurement of
small parameters
Communication
Sound
propagation
Drug patent
applications
Material research,
crystallography
Reference/source
Astronomy_Collimation_
Good.jpg
Meter
Parasitol Res (2007) 101:1393–
1399
http://www.springerlink.co
m/content/xt0225m1w4745
6r0/fulltext.pdf
Goniometer
Electron
microscope
Crystallography_RHEED
_setup.gif
Crystallography_Bragg_
Diffraction.png
Crystallography_Lauegr
am_Si_100_4foldSymm_Inclined.png
Crystallography_Lauegr
am_4-foldSymmetry.jpg
Crystallography_Lauegr
am_Si_111_3foldSymm.jpg
Crystallography_Lauegr
am_6-foldSymm.jpg
Crystallography_Debyeg
ram_Powder.jpg
Diffraction effects - 25
Table: Material research, crystallography – various methods:
Diffracting
particles
Diffraction method
Typical
depth
Electrons
Electron microscopy
Surface layers Surface
research of
crystalline
materials with
an electron
microscope in
the diffraction
mode
Low energy
electrons
LEED
Surface layers Surface
research of
crystalline
material
High energy
electrons
RHEED
Several outer
thin layers
(eg. Watching the growth of thin layers within MBE)
(nanometers)
Usage
Fabrication of
integrated
circuits, chips,
etc.
X-ray photons
XRD (X-ray diffraction)
Several
micrometers
Crystallography
Neutrons
Neutron diffraction
Several
centimeters,
interaction
with the
magnetic
moments of
atomic nuclei
Crystallography
and magnetic
structures
research
Diffraction effects - 26
Diffraction is widely used in materials research and crystallography; various
diffracting particles create a Fourier transform image of real material structure
in typical depths (from surface layers to several centimetres – see the table
above). Moreover, neutrons help to determine magnetic structures, because
they interact with the magnetic moments of atomic nuclei.
The RHEED (Reflection High Energy Electron Diffraction) method is used with
the MBE (Molecular Beam Epitaxy) to observe the growth of thin layers and to
count them within the fabrication of integrated circuits or chips.
Fig. RHEED method for the observation of growth of thin layers. When the
upper thin layer is finished, we can see one big diffraction peak, otherwise
there are more smaller peaks visible.
The structure of proteins is important for the development of new medications.
Therefore a diffractogram must be attached to the patent application.
Diffraction is important for astronomy, astrophysics, and spectroscopy. Prisms
in spectroscopes are suitable for overview spectra of wide range in wavelength
because of lower resolution. We can reach higher resolution in wavelength
only with gratings. Astronomers use diffraction rings of a out-of-focus star for
the collimation of optical axes of their telescopes (usually Cassegrain-like
telescopes).
Finally, let‟s answer the introductory question about the unnatural four-spike
stars in the astrophotography.
Diffraction effects - 27
Spikes are the resulting diffraction pattern originated from the usual
secondary mirror spider (holder) that must have four (theoretically also two)
perpendicular arms because the Fourier transform image follows the
symmetry. For three arms (with 120 degrees) there would be six-spike stars
on the astrophotography. To avoid this disturbing effect one can fix the
secondary mirror to the meniscus (Maksutov-Cassegrain optical system) or
Schmidt correction lens or one can use curved holder like in figures below
instead of traditional ones.
Diffraction effects - 28