31. electromagnetic waves and refraction
TRANSCRIPT
31. Electromagnetic waves and refraction
www.ariel.ac.il
• A Capella today
• Some history
• McLeap Part 1 due tomorrow
• In-class quiz on Friday
Structure of final exam:
~15 conceptual questions (like pre-lecture quizzes, in-class polling and in-class quiz 2)
(30 mins)
~15 Application of formula questions (like McLeap and in-class quiz 1)
(50mins)
~5 Problems subdivided in smaller problems (like assignments and in-class quiz 3)
(100mins)
Alien (or other) sources of radiation:
Tesla measured the first out of space radio signal
Ref: André Waserwiki
Tesla measured the first out of space radio signal
In 1967 PhD student Jocelyn Bell discovered the source of the radio signal (pulsar)
Ref: André Waserwiki
BigEarr.com
Lurgan college…
Crab Pulsar (wiki)
Daniel A. Russell
Sound waves are longitudinal waves:
http://www.ariel.ac.il/
Electromagnetic waves are transverse waves:
Can wifi radiation be bad for you?
A. Yes
B. No
C. Maybe
National Radio Quiet Zone
Superposition of different wave-lengths can create a periodic pulse:
Superposition of different wave-lengths can create a periodic pulse:
Physics Nobel prize 2018: jointly to Gérard Mourou and Donna Strickland "for their method of generating high-intensity, ultra-short optical pulses.
Source: Nobelprize.org
Refraction (demo and history):
The image shows his discovery of the law of
refraction. Ibn Sahl (c. 940-1000) was a
Persian Mathematician in the court of
Baghdad. About 984 he wrote a treatise On
burning Mirrors and Lenses in which he set
out his understanding of how mirrors and
lenses bend and focus light. In his work he
discovered a law of refraction. He used his
law of refraction to compute the shapes of
lenses and mirrors that focus light at a
single point on the axis.
Source:
THE DIGITAL INSTITUTE OF THE A
RTS
dt
d2
ninr
“Ibn Sahl law”𝑑2𝑑𝑡
=𝑛𝑖𝑛𝑡
d
GlassAir
dt
dt
d2
θi
nint
“Ibn Sahl law”𝑑2𝑑𝑡
=𝑛𝑖𝑛𝑡
d Geometry: sin(θi)=𝑑
𝑑2
GlassAir
dt
dt
d2
θt
nint
“Ibn Sahl law”𝑑2𝑑𝑡
=𝑛𝑖𝑛𝑡
d Geometry: sin(θt)=𝑑
𝑑𝑡
GlassAir
dt
dt
d2
θt
θi
nint
“Ibn Sahl law”𝑑2𝑑𝑡
=𝑛𝑖𝑛𝑡
d Geometry: sin(θt)=𝑑
𝑑𝑡and sin(θi)=
𝑑
𝑑2
GlassAir
dt
dt
d2
θt
θi
“Snel’s law”
nint
“Ibn Sahl law”𝑑2𝑑𝑡
=𝑛𝑖𝑛𝑡
d Geometry: sin(θt)=𝑑
𝑑𝑡and sin(θi)=
𝑑
𝑑2
sin(θt)
sin(θi)=𝑛𝑖𝑛𝑡
GlassAir
dt
Thomas Harriot (Oxford, c. 1560 – London, 2 July 1621) — or
spelled Harriott, Hariot, or Heriot — was an English
astronomer, mathematician, ethnographer, and translator. He is
sometimes credited with the introduction of the potato to the
British Isles. Harriot was the first person to make a drawing of
the Moon through a telescope, on 26 July 1609, over four
months before Galileo.
Apart from the correspondence with Kepler, there is no evidence
that Harriot ever published his detailed results on refraction. His
personal notes, however, reveal extensive studies significantly
predating those of Kepler, Snell and Descartes. Harriot carried
out many experiments on refraction in the 1590’s, and from his
notes it is clear that he had discovered the sine law at least
as early as 1602. Around 1606, he had studied dispersion in
prisms (predating Newton by around 60 years), measured the
refractive indices of different liquids placed in a hollow glass
prism, studied refraction in crystal spheres, and correctly
understood refraction in the rainbow before Descartes
Source: J. M. Dudley and A. M. Kwan and Wiki
Snel’s law: If the eye O (in the air) receives a light ray coming from a point R in a medium (for example, water) and refracted at S on the surface A of the medium, then O observes the point R as if it were at L on the line RM⊥ surface A. Then SL:SR is constant for all rays. This agrees with the present formulation of the law, which states that sin r: sin i is constant, where i and r are the angles that OS and SR make with the normal to A at S. (source: Encyclopedia.com)
SNEL (SNELLIUS OR SNEL VAN ROYEN), WILLEBRORD
(B. Leiden, Netherlands, 1580; d. Leiden, 30 October 1626),
mathematics, optics, astronomy.
Snel was the son of Rudolph Snellius, or Snel van Royen, professor of
mathematics at the new University of Leiden, and of Machteld
Cornelisdochter. He studied law at the university but became interested in
mathematics at an early age.
The arrangement was that he should take over the teaching duties since his father was too ill to continue but, should his
father recover, he had to stand down. Since Rudolph died a month later, Snell was required to continue teaching but he
struggled to get proper recognition from the University of Leiden. He received a higher salary in February 1614 but was
still getting between 1/3 and 1/2 of the salary of other professors. He was made a full professor of mathematics in February
1615 but his salary was not increased. Slowly he received increases but only in 1618 did he receive what he considered
the proper amount for his position. Source: http://www-groups.dcs.st-and.ac.uk
In 1615 Snellius, after the work of Eratosthenes in Ptolemaic
Egypt in the 3rd century BC, probably was the first to try to
do a large scale experiment to measure the circumference of
the earth using triangulation. He was helped in his
measurements by two of his students, the Austrian barons
Erasmus and Casparus Sterrenberg. In several cities he
also received support of friends among the city leaders
(regenten). In his work The terrae Ambitus vera
quantitate (1617) under the authors name ("The Dutch
Eratosthenes") Snellius describes the methods he used. He
came up with an estimate of 28,500 Rhineland rods (nl) - in
modern units 107.37 km for one degree of latitude. 360
times 107.37 then gives a circumference of the Earth of
38,653 km. The actual circumference is 40,075 kilometers,
so Snellius underestimated the circumference of the earth
by 3.5%. Source: wikiwand
Snel’s measurement of the circumference of the
Earth
Quadrant of Snel measured angles to a
precision of 0.1 degrees
Descartes
1678 Traité de la Lumière, Christiaan Huygens
In his 1678 Traité de la Lumière, Christiaan Huygens showed how Snell's law
of sines could be explained by, or derived from, the wave nature of light, using
what we have come to call the Huygens–Fresnel principle.
As the development of modern optical and electromagnetic theory, the ancient
Snell's law was brought into a new stage. In 1962, Bloembergen showed that
at the boundary of nonlinear medium, the Snell's law should be written in a
general form. In 2008 and 2011, plasmonic metasurfaces were also
demonstrated to change the reflection and refraction directions of light beam.
Source: Wiki
René Descartes independently derived the law using heuristic momentum
conservation arguments in terms of sines in his 1637 essay Dioptrics, and used it to
solve a range of optical problems. Rejecting Descartes' solution, Pierre de
Fermat arrived at the same solution based solely on his principle of least time.
Interestingly, Descartes assumed the speed of light was infinite, yet in his derivation
of Snell's law he also assumed the denser the medium, the greater the speed of
light. Fermat supported the opposing assumptions, i.e., the speed of light is finite,
and his derivation depended upon the speed of light being slower in a denser
medium. Fermat's derivation also utilized his invention of adequality, a
mathematical procedure equivalent to differential calculus, for finding maxima,
minima, and tangents.
Descartes derivation is based on momentum conservation, while Fermat used the
least action principle (shortest time).
Modern theory: Quantum Electro-Dynamics (QED) by Pauli, Schwinger,
Feynman, Tomonaga and Dyson,… Describes light and matter interactions.
ℒ =1
2𝜇0−1
𝑐2𝐸2 + 𝐵2 + ത𝜓[𝑖 𝜕 − eA −m]ψ
Lagrangian
Free fieldselectrons
Electron-
E&M field
Feynman diagram
representing Coulomb’s
interaction
In the modern theory of physics (Quantum Field Theory and the so-called
standard model, since 1970s) all particles (photons, electrons, protons,
quarks,…) are described by quantum fields (except gravitons).
It’s a bit like the photons that are described by their Electromagnetic fields
(the quantum version).