Title: Developing ideas of refraction, lenses and rainbow through the use of Medieval Resources of Arabs and Persians
1Developing ideas of refraction, lenses and
rainbow through the use of Medieval Resources of
Arabs and Persians
- Pavlos Mihas
- Democritus University
2Learning to apply a law
- Usually students do not learn to apply general
principles. - In optical phenomena there is a need to learn to
apply at least qualitatively Snells law. - There are some useful approximations
- This approximation holds up to 40
3Usefulness of a law
- It is good to have an idea of what are the values
expected. - This helps the students to repeat a measurement.
- A comparison with Historical measurements also
helps to see how well they perform - So we do measurements and compare with law
like relations and historical data.
4Historical data and methods
- Ptolemys method A semicircle and 3 pins
- At first we put a pin B at the center and then we
choose the angle of incidence where we put A. A
pin C is moved along the curved side until the 3
pins overlap. - Usually it works well up to 80.
5Extensions of Ptolemys law
- The same idea can be applied to other shapes
6Which Law?
It seems that Ptolemy gave results that have
constant Differences of the Increase of the
Refraction Angle
Does this hold also for his air to glass data?
7Ptolemys results and quadratic law
Students measurements can be very well fit in a
quadratic law
8Why we have to believe Snells Law?
- At this point we can stress the importance of
theory in experiments - Scientists design their experiments according to
the theory they hold. - The data they collect reflect the theory or Law
they believe. - Ptolemy believed in visual Rays ??e??, while Al
Haytham ??????? believed that light comes to our
eyes from the bodies.
9Al Haythams method
- Al Haytham employed a light beam. He used two
diaphragms (UHF, hole on MPQN) to make a
parallel beam - He measured the angle of deviation KCI
- He did not give one general relation but some
rules. - His rules are not accurate for ranges that exceed
Ptolemys results. - Students can check Al Haythams rules
10Checking Al Haythams rules
- In rare to dense refraction, deviation anglelt1/2
incidence angle
11Interpretation of the Law
- Corpuscular Interpretation
- Wave Interpretation
12Al Haythams interpretation
- Al Haytham proposed a corpuscular interpretation
- He expressed the idea of vector Analysis There
is a portion (??? koust) of velocity in a
direction parallel to the surface and a portion
perpendicular to the surface . - According to Al Haytham, light must be deviated
toward the path of least resistance. - The resistance is smallest in the direction
perpendicular to the surface. - If refraction is a weaker case of reflection, why
refraction is not away from the perpendicular?
13Newtons Interpretation
- A kind of gravitational field exists.
- This field accelerates the particles when they
enter in a denser medium, and decelerates them
when they enter into a rarer medium. - When the particles exit then they are decelerated.
This interpretation avoids all the difficulties
that were presented by Al Haythams treatment. It
can be used to describe the behavior of lenses
and prisms.
14Which model to teach?
- In a 8th grade Greek textbook is presented
Fermats principle. - In a 7th grade Albanian textbook is presented a
corpuscular theory.
15Which model for refraction?
- It is inconsistent to teach refraction with a
particle model
16Wave model vs. corpuscular model
- Wave model is easier to understand and gives a
grasp to the interested students. - Corpuscular model is misleading. It directs the
students thought to classical bodies. For
example the explanation of the shadow in
comparison to rain or dust. - Photon model should be taught because of
quantum mechanics, but the ideas of quantum
probabilities and Feynmans path integrals are
not appropriate for students of 7th of 8th grade.
17Refraction and the problem of focusing
- Ibn Sahls law of refraction
18Ibn Sahls perfect focusing
19Refraction on a Sphere Special rays
If we consider the point where the ray meets the
sphere after refraction we can see
A that there is a limit for a special angle
of incidence. Rays with a larger incidence angle
meet the sphere at a point nearer to the axis.
The PARALLEL rays cut the SPECIAL ray either
inside the sphere or outside. Geometrically we
have
- The ray that Al Haytham proposed as a limiting
case was employed by Al Farisi to divide the
incident rays to the exterior and interior cone.
20Refraction and the Rainbow
21Refraction and Observations
- Al Haythams Theory about the influence of
atmospheric refraction on the observation of
astronomical phenomena - Al Haytham proposed that the atmosphere causes a
refraction of the light. This causes a change
in the angle where the Moon is seen.
22Al Haythams model
- He proposed several factors for the change of the
appearance - Refraction by air
- Possibility of existence of a layer of vapors
over the atmosphere. - Possibility of an error of observation
23What model for the atmosphere
24Atmosphere Vapors