physics programs by PAVLOS MIHAS, 
Department of Primary-Level Education
, DEMOCRITUS  University of Thrace (DUTH)

The following programs were created in a Visual Basic Environment (if you do not want to download the exe files to ask for zip files)

There are programs on: coils, rotating frames, waves, OPTICS (Huygens' principle, Huygens construction of  lens for perfect focusing, Fermat's principle plus Huygens, curved mirrors, concave mirrors, eclipses, Refraction, lenses, Rainbow, Penumbra Determination of focal lengths), CHEMISTRYAl Haytham's Problem (AlHazen's Problem) and Huygens' solution to it

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a)Induction on Coils

Click on INDUCTION for the induction program. (Published in Physics Education, January 2003)

b) Mechanics and Rotating frames

Program neil_curve.exe that examines the curve proposed by William Neile. For a special value of the velocity (called alfa) the vertical component remains constant.
The student can see that the radius o curvature decreases and becomes zero at the top. The centripetal acceleration becomes infinite.

Program sinusoidal: examines the factors that affect centripetal acceleration

Program kykloeides.exe and cycloid.exe (newer edition of kykloeides) shows 1) The size of the radius of curvature of the cycloid pendulum compared to the cyclical pendulum
                                                2) The 2 pendulums as they vibrate. TDescription: Description: Description: Description: rotatinghe cyclical follows the exact solution (wDescription: Description: Description: Description: ROTATINGith elliptic functions)

Program KENTRO_bMAGNET.exe show the evolution of the path of a charged body in a magnetic field. It can also be used in conjunction
with the program rotating_English to show the Foucault pendulum

Click on rotating_frame for a program of rotating frames which examines friction and pseudo - forces. Other topics: Foucault's pendulum, kinematics on 2 dimensions.
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c) Waves: A program SEISMIC_P.exe shows the propagation of waves in a medium where the speed changes with the depth.

for longitudinal waves depicting the rays and Waves fronts. It is useful in connection with teaching the change of speed (in sound waves, as in change of velocity due to gradual temperature change) and in seismic waves. Another program longitudinal.exe (108 kB) examines the propagation of a pulse. It is possible to have two different media. The end can be fixed or free. This helps to explain why a rarefaction pulse (depression in Seismology) causes the ground to move downwards when the first pulse arrives, while a compession pulse causes the ground to move upwards

The program:curved_radii.exe gives an animated display of wave fronts with two different dependencies of the speed of the wave with depth.

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The software KYMATA.EXE helps the study of the transmission (from right to left) of TRANSVERSE wave pulses and the study of reflection at fixed or free end.

For the wave pulses the EXCEL file pulses REFLECTION AND REFRACTION.XLS gives the forms of wave pulses as they travel from one medium to another

For the wave fronts the EXCEL file GRADUAL CHANGE.xls  gives the form of rays when the wave speed is not constant
d) Optics programs

1.     The first program deals with Al Haytham's theory of the appearance of the meniscus of Sun's eclipse on the screen of a pinhole camera. You can find some information on this in the article by  Pavlos Mihas(2001): A historical example of the use of the 'pinhole camera',  pp 19 - 21, SCHOOL SCIENCE REVIEW -July 2001
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The second pr gram deals with Al Haytham's theory on the nature of the Moon's surface .Description: Description: Description: Description: moon
The question was: Does the moon reflects like a mirror or it reflects diffusively?
This program expands on Al Haytham's ideas 


You can find explanations on the model in the article by Pavlos Mihas (2002):  Some historical resources for teaching about curved mirrors, PP 311-317, PHYSICS EDUCATION, July 2002 (available from the site of Physics Education

  1. The third program deals with Al Haytham's treatment of concave mirrors.
    It presents two contributions by Al Haytham:
    a) The composite spherical mirror. In this program you will examine how Al Haytham dealt with the fact that actually there is not a point focus for spherical mirrors - as opposed to parabolic.
    b) Al Haytham's question of how many points on a mirror can join through reflection two given points
    The program is:


You can find explanations on the model in the article of PHYSICS EDUCATION, July 2002 mentioned in # 2.
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   4. A program examining the history of the law of REFRACTION. In this program there is an option for the examination of ERRORS, another option for HISTORICAL MEASUREMENTS. In the HISTORICAL notes are included the PTOLEMY'S method for determining the angles of REFRACTION which is essentially the method of pins, Al HAYTHAM'S method of determining the angles of refraction which is the method of light bundles. DIATHLASI.exe

You can find explanations in the article by Pavlos Mihas (2001): Educational Software Connecting History of Optics with the Optics Laboratory, THEMES IN EDUCATION  Volume 2 - Number 1, 2001 pp 59 - 70 (Publisher LEADER Books, You can find information on the Themes In Education on the site of the University of Ioannina: or on the site of Leader books: Also presented in Leeds at the 8th History and Philosophy of Physical Sciences in Science Teaching (July 2005)

  5. A program which examines the properties of spherical lenses and IBN SAHL'S (9th century) HYPERBOLIC LENS FAKOI.
Another version of this program shows the thin lens model and the thick lens model

The article by Pavlos Mihas (2003): Using History in Teaching Optics, pp 15 - 23 in THEMES OF EDUCATION volume 4 - Number 1 refers to the use of History in teaching Optics. Also presented in Leeds at the 8th History and Philosophy of Physical Sciences in Science Teaching (July 2005)
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  6. A program which examines the ideas of AL FARISI who in the 14th century presented the first mathematical theory for the shape of the rainbow 2 centuries before DESCARTES. This program shows the refraction and reflection in the interior of a sphere toxo

. See Pavlos Mihas (2003)Also presented in Leeds at the 8th History and Philosophy of Physical Sciences in Science Teaching (July 2005)

7. A program that examines and expands the ideas of AL HAYTHAM on the intensity of light in a PENUMBRA

8. A program that examines the effect of the atmosphere on the observation of the Moon. The index of refraction can be change abruptly for 1 to n, or gradually. There is also a possibility for the existence of a layer of vapors according to AL HAYTHAM. The program is SIZE_HEIGHT_MOON

 9.  Determination of focal lengths: An Excel file contained in the file focal . This Excel file contains macros which should be activated .
These macros permit the user to find all the cuts of the lines x/a+y/b=1 (which are drawn between the points (a,0) and (0,b))where a is the distance ofthe objec

t from a lens (or concave mirror) and b is the distance of the image (or screen). This file is useful because these lines do not intersect at one point (f,f) but give a constellation of intersections.  Sometimes students "cheat" on their plots trying to show  better results. If the instructor inputs the a,b in this file and press the button "plot all points of cuts" can give to the student a visualized lesson on statistical concepts like mean value and standard deviation. (There is a short article in Computer Education November 1998 on this.)
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10. Description: Description: Description: Description: huygensHUYGENS' PRINCIPLE   Shows the wavelets that combine to give a wave front

The article "The problem of focusing and real images" was published in the European Journal of Physics (Eur. J. Phys. 29 (2008) 539-553.)
and is available at: contains the subject of Huygens's principle, Fermat's principle, Al Haytham's problem.


Description: Description: Description: Description: huygens lens11.Huygens construction of  lens for perfect focusing Uses the method presented in "La TRAITEE Description: Description: Description: Description: hyperbolicDU LUMIERE   It is in two forms: Huygens  Lens which shows the shape of a lens with rays and wave fronts and  Huygens Lens Construction which permits to the students to draw a lens (with a circle or an hyperbola on the left side)






Description: Description: Description: Description: C:\Users\Pavlos Mihas\Documents\PAVLOS'S DOCUMENTS\ARXES FYSIKHS 2011 2012\Arxes fysikhs gia web\english\figure-12.gif12. Fermat's principle: Shows how Fermat's principle can be applied in conjunction with Huygens' principle to find the point where the rays or wavefronts converge. It is included in the software lenses (

A similar program shows also the thin lens model with a cross and the thick lens approximation.

An excel file gives the student the idea that when a ray follows Snell's law then the time is minimum

A special case for Hero's principle (which is the case of Fermat's principle in case of reflection) is examined in the file PARABOLA ELLIPSE.xls:




d) chemistry

A program developed by P. Michas and G. Papageorgiou is "CHEMKIN" (0,98 MBytes) and the zip file is CHEMKINZIP (1,8 MB) This program examines the factors that influence the speed of chemical reactions and radioactivity. You can find explanations in the article by P. Michas and G. PapageorgiouSCHOOL SCIENCE REVIEW, July 2001
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