Four hands-on activities obeying the inverse square law Sarantos Oikonomidis Dimitrios Sotiropoulos Nikolaos Voudoukis George Kalkanis University of Athens Pedagogical Department Laboratory of Science Technology and Environment 13a Navarinou St. Athens GR

The motive – The question Is it possible to find lab activities which bring out unification and a non piecemeal description of physical phenomena? So we want to find hands-on activities to help our students in order to understand the cohesion in Nature and to export conclusions from experimental data.

The inverse square law Point-like sources of gravitational forces, electric fields, light, sound and radiation obey the inverse square law. This geometrical law gives the ability of unifying educational approach of various cognitive subjects in all the educational levels.

The inverse square law. I is the intensity in r distance, that corresponds to a surface A. At a 2r distance the same amount of energy pass through the surface 4A. So the intensity becomes I/4 etc.

Educational methodology We suggest the inquiringly evolving educational model (Kalkanis 2002), that includes the following steps: 1. Trigger of interest 2. Hypothesis expression 3. Experiments 4. Formulation of conclusions and proposals - recording 5. Generalisation - feedback - control

Activity 1 The inverse square law as a geometrical law Materials: a cardboard with grid, a cardboard with a hole, supporting clips, ruler, candle. Students observe and they count the lighted squares on the cardboard with the grid at different distances between the candle and the cardboard with the grid.

Activity 2 Building a photometer Verification of the inverse square law for the light Materials: 2 pieces of paraffin oil, ruler, four light bulbs, two rubbers, aluminum foil. We put the aluminum foil between the two pieces of paraffin. We put two of the light bulbs in one meter distance between them. The students measure the distances of the bulbs from the photometer when the luminosity is the same from the two sides of the photometer

P1 :power of Lamp1 d1 :distance between lamb1 and photometer d2 :distance between lamb2 and photometer The same luminosity means the same intensity of light. P1(W)P2(W)P1/P2d1(cm)d2(cm)d1/d /150 1/ / / / / / /57

Activity 3 The inverse square law about the intensity of light using sensors Real-Time experiment Aim: To find the relation between the intensity of light and distance. Materials: Computer, light sensor, position sensor, lamp, software (coach 5).

Activity 4 The inverse square law using a radioactive source Aim: To ascertain the validity of the law also in electromagnetic radiation that emits from radioactive sources using a Geiger-Miller. Materials: Radio active Co60 5μCi, Geiger Muller, ruler.

Using the Geiger Muller we took stand radioactivity measurements for two minutes in two vertical directions. There has been taken five different measurements for each direction. Continuously we used a radioactive source Co_60 5μCi and took five measurements for 2 minutes period in two different distances 20 cm and 40 cm. The data confirmed satisfactory the inverse square law. Measurements with the radioactive source of Co_60 5μCi without the stand radioactivity. The data confirmed satisfactory the inverse square law.

Conclusions The intensity of light decreases as we go away from the source of radiation and obeys the low I=k/r2. Intensity (lux) Distance (m) 1600, , , , ,62 87Ο,67 800,70 600,84 401,12 301,40

Generalisations We can apply this to study: The magnitude of a star The absolute magnitude of a star. The eye as a logarithmic detector The inverse square law for gravitational and electrical forces and it’s relation to the gravitons and photons respectively.

The above procedure was applied to the students of Pedagogical Department of University of Athens, through a non fragmentary but unified approach. The results were satisfying and the activities will be included in laboratory exercises for the students in the academic year of The stand radioactivity measurement was already included since 2005.