Pavlos Mihas Democritus University
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Transcript of Pavlos Mihas Democritus University
Developing ideas of Developing ideas of refraction, lenses and refraction, lenses and
rainbow through the use rainbow through the use of Medieval Resources of of Medieval Resources of
Arabs and PersiansArabs and Persians
Pavlos MihasPavlos Mihas
Democritus UniversityDemocritus University
Learning to apply a law
Linear approximation
incidenceofanglerefractionofangle3
2
This approximation holds up to 40°
Quadratic approximation
angleincidencebangleincidenceanglerefraction ²0025,0
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?PTOLEMY’S RESULTS FOR
REFRACTION FROM AIR TO WATER
Angle of Incidence
Angle of Refraction
Increase in the Angle of Refraction
Difference of Increase
0° 0° 8°00’
10° 8° 30’ 7°30’
20° 15°30’ 30’ 7°00’
30° 22°30’ 30’ 6°30’
40° 29° 30’ 6°00’
50° 35° 30’ 5°30’
60° 40°30’ 30’ 5°00’
70° 45°30; 30’ 4°30’
80° 50°
PTOLEMY’S RESULTS FOR REFRACTION FROM AIR TO
GLASS Angle of Incidence
Angle of Refraction
Increase in the Angle of Refraction
Difference of Increase
0° 0° 7°00’
10° 7° 30’ 6°30’
20° 13°30’ 30’ 6°00’
30° 19°30’ 30’ 5°30’
40° 25° 30’ 5°00’
50° 30° 30’ 4°30’
60° 34°30’ 30’ 4°00’
70° 38°30; 30’ 3°30’
80° 42°
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 lawy = -0,0025x2 + 0,725x
R2 = 1GLASS
y = -0,0025x2 + 0,825x
R2 = 1WATER
0
10
20
30
40
50
60
0,00 20,00 40,00 60,00 80,00
INCIDENCE ANGLE
RE
FR
AC
TIO
N A
NG
LE Angle of Refraction
WATER
Angle of RefractionGLASS
Quadratic (GLASS)
Quadratic (WATER)
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 rulesChecking Al Haytham’s rules•In rare to dense refraction, deviation angle<1/2 incidence angle
Interpretation of the LawInterpretation of the Law
Corpuscular InterpretationCorpuscular Interpretation Wave InterpretationWave Interpretation
Al Haytham’s interpretationAl 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 InterpretationNewton’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?Which model to teach?• In a 8th grade Greek textbook is
presented Fermat’s principle.• In a 7th 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?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 Wave model vs. corpuscular modelmodel
• 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 7th of 8th grade.
Refraction and the problem Refraction and the problem of focusingof focusing
• Ibn Sahl’s law of refraction
Ibn Sahl's expression of Snell's law
Ibn Sahl’s perfect focusingIbn Sahl’s perfect focusing
Ibn Sahl’s Hyperbolic Lens
Refraction on a Sphere: Special raysRefraction 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.
ci
ci
ci
cinn
lim
lim(
2
1
))sin(
arcsin)sin(
arcsin
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 seeA 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 RainbowRefraction and the Rainbow
External and Internal cones of Al Farisi
Refraction and ObservationsRefraction 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 modelAl 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 What model for the atmosphere:atmosphere:
Atmosphere: VaporsAtmosphere: Vapors