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

Learning to apply a law Linear approximation This approximation holds up to 40° Quadratic approximation Usually students do not learn to apply general principles. In optical phenomena there is a need to learn to apply at least qualitatively Snell’s law. There are some useful approximations:

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.

Historical data and methods Ptolemy’s 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°.

Extensions of Ptolemy’s law The same idea can be applied to other shapes

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?

Ptolemy’s results and quadratic law s Students measurements can be very well fit in a quadratic law

Why we have to believe Snell’s 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” ὄψεις, while Al Haytham الهىثام believed that light comes to our eyes from the bodies.

Al Haytham’s 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 Ptolemy’s results.  Students can check Al Haytham’s rules

Checking Al Haytham’s rules In rare to dense refraction, deviation angle<1/2 incidence angle

Interpretation of the Law  Corpuscular Interpretation  Wave Interpretation

Al Haytham’s interpretation Al Haytham proposed a corpuscular interpretation He expressed the idea of vector Analysis: There is a portion ( قسط 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?

Newton’s 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 Haytham’s treatment. It can be used to describe the behavior of lenses and prisms.

Which model to teach? In a 8 th grade Greek textbook is presented Fermat’s principle. In a 7 th grade Albanian textbook is presented a corpuscular theory. Particle model for reflection in Prifti et al (2003): elastic ball on the left impinging on the floor and light on the right impinging on a mirror

Which model for refraction? It is inconsistent to teach refraction with a particle model Refraction of sound in water (air in the upper part) (Prifti et al 2003). On the right is shown a wave refraction

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 student’s 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 Feynman’s path integrals are not appropriate for students of 7 th of 8 th grade.

Refraction and the problem of focusing Ibn Sahl’s law of refraction Ibn Sahl's expression of Snell's law

Ibn Sahl’s perfect focusing Ibn Sahl’s Hyperbolic Lens

Refraction on a Sphere: Special rays 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. Relation of rays to the special ray of critical angle of incidence. Rays with a larger incidence angle meet the sphere at a point nearer to the axis. 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 The PARALLEL rays cut the SPECIAL ray either inside the sphere or outside. Geometrically we have

Refraction and the Rainbow External and Internal cones of Al Farisi

Refraction and Observations Al Haytham’s 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.

Al Haytham’s 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”

What model for the atmosphere:

Atmosphere: Vapors