Developing ideas of refraction, lenses and rainbow through the use of Medieval Resources of Arabs and Persians - PowerPoint PPT Presentation

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Developing ideas of refraction, lenses and rainbow through the use of Medieval Resources of Arabs and Persians

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Title: Developing ideas of refraction, lenses and rainbow through the use of Medieval Resources of Arabs and Persians


1
Developing ideas of refraction, lenses and
rainbow through the use of Medieval Resources of
Arabs and Persians
  • Pavlos Mihas
  • Democritus University

2
Learning 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
  • Linear approximation
  • This approximation holds up to 40
  • Quadratic approximation

3
Usefulness 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.

4
Historical 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.

5
Extensions of Ptolemys law
  • The same idea can be applied to other shapes

6
Which 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?
7
Ptolemys results and quadratic law
Students measurements can be very well fit in a
quadratic law
8
Why 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.

9
Al 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

10
Checking Al Haythams rules
  • In rare to dense refraction, deviation anglelt1/2
    incidence angle

11
Interpretation of the Law
  • Corpuscular Interpretation
  • Wave Interpretation

12
Al 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?

13
Newtons 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.
14
Which model to teach?
  • In a 8th grade Greek textbook is presented
    Fermats principle.
  • In a 7th grade Albanian textbook is presented a
    corpuscular theory.

15
Which model for refraction?
  • It is inconsistent to teach refraction with a
    particle model

16
Wave 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.

17
Refraction and the problem of focusing
  • Ibn Sahls law of refraction

18
Ibn Sahls perfect focusing
19
Refraction 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.

20
Refraction and the Rainbow
21
Refraction 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.

22
Al 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

23
What model for the atmosphere
24
Atmosphere Vapors
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