All 3 entries tagged Physics Lesson
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April 10, 2011
Teaching geometric optics of mirrors and lenses
Geometric optics
GeoGebra is very useful for illustrating the principles of geometric optics. The GeoGebra construction sequence of the ray diagram differ very little from textbook description. The only difference is that the GeoGebra page is interactive and works for other scenarios. The GeoGebra page allows the investigator to explore the effect on the image when the position of the object or focal length is varied. There is no need to reconstruction another ray diagram for every variation. One construction covers all scenarios! This is powerful demonstration of the generality of construction principle.
The constructions are fairly straightforward. The pages below include a construction step toolbar. Press the play button to playback the construction sequence. There are three different ways to use the GeoGebra pages for teaching. (1) The pages can be used as presentations in the lesson. (2) Students can use the pages as simulations of optics experiments. (3) The pages are benchmarks for what could be emulated by the GeoGebra. Students could construct similar pages as projects.
Concave mirror 
Convex mirror 


Converging lens 
Diverging lens 
The pages (click to open a separate page for the actual GeoGebra pages) were created for demonstration in a physics lesson and for students to investigate the properties of the mirrors and lenses. In addition to the mirrors and lenses, the following pages of the parabola and prism were created to illustrate the design principles of the optical elements. The mirrors are based on the mathematics of parabola. The lenses are based on the physics of the refraction described by Snell's law.
Parabola
This dynamic geometry page shows that a parabola is a locus of a point P which is equidistant to the focus F and a point G on the directrix d. PG is parallel to the xaxis. The lengths of PF and PG are equal, therefore the FGP is an isosceles triangle. b, the perpendicular bisector FG is the tangent to the locus. This properties is important in Physics. A ray incident in parallel to the xaxis of the parabolic mirror is reflected to to the focus F. The reverse is also true because a ray is reversible.
In this construction, F' is a reflection of F about yaxis. Therefore, the parabola will always passes through the origin. Move F on the xaxis will change the curvature of the parabola.
Prism
This simulates the refraction of light in a glass prism using Snell's law. The refractive index is adjustable and glass prism can be transformed into a trapezoidal or triangular prism. The page is capable of producing two totally internal reflections inside the prism. The page aims to illustrate the concept that the crosssection of a converging or diverging lens resembles a glass prism. Focusing the light at the focus is the result of the application of Snell's law.
It was a "Tour de force" of GeoGebra skill to produce the page. There are 105 construction steps. There is a maximum of two refraction and reflection points on each side of the trapezium. Thus, the physics simulated by the page is correct up to a limit. The page should not be used by students unsupervised and teachers should explore many different scenarios to prepare for any surprise. Snell's law is simulated using a string of commands "Rotate[R_1, If[abs(n sin(Angle[R', R, R_2])) ≤ 1, asin(n sin(Angle[R', R, R_2])), Angle[R', R, R_2]  π], R]" for the refraction of light at the point R. R_1 and R_2 are points at the end of the interfacial normal at R. Each refraction/reflection point can accept an incident ray from another reflection points.
March 13, 2011
Teaching energy, power and efficiency in physics
The picture shows a snapshot of a dynamic work sheet to support classroom discussion on the topic of workdone, power and efficiency in a Physics lesson. The animals pull along some loads for some distances. Students are encourage to discuss the merit of which animal did most work, which was most powerful and which worked most efficiently. They are encourage to give reasons to support their assertions. Pressing the star buttons at the bottom of screen will reveal the answers graphically and numerically.
The performances of the animals are determined anew randomly every time the program is restarted. The size of the animals is not an indicator. However, the size of the food is directly proportional to the energy it contains. Energy which is the product of force and displacement is presented by the area of a rectangle. Power is how much the energy is output per unit time. Efficiency relates the energy output to the how much food the animal has eaten. Scratch was used to create the work sheet. It is quite popular and is quite easy to use.
October 28, 2010
Cloud chamber experiment
A very successful experiment demonstrated the alpha particle radiation using a cloud chamber in the Westwood Teaching Building! The radioactive source was placed at the head of a bended pin which was pierced into a cork. The photograph on the left showed the cloud chamber apparatus. The photograph on the right showed four bright spots. The brightest spot where the tracks of the condensation originated was the pin head holding the radioactive source. The remaining three spots were multiple reflections of the pin head of the chamber and my camera (see my gallery for more pictures).
