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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-106 80
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
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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/P2 d1(cm) d2(cm)
d1/d2
100
100
1/1
50
50
1/1
75
100
3/4
46
54
46/54
40
100
2/5
39
61
39/61
40
75
8/15
43
57
43/57
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)
160
0,42
140
0,50
130
0,52
120
0,56
100
0,62
87
Ο,67
80
0,70
60
0,84
40
1,12
30
1,40
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 2007.
• The stand radioactivity measurement was
already included since 2005.