Announcements:

• This week: Nature and propagation of light (light and refraction)• Reminder: Lab 4 (optics) started yesterday. Print the handouts for your lab session• No pre-lecture quizzes this week.• Assignment 4 (McLeap part 2) starting later today due on Monday.

Lab 3 (AC circuits) was interesting

A. Strongly agree

B. Agree

C. Neutral

D. Disagree

E. Strongly disagree

The equipment in lab 3 worked well

A. Strongly agree

B. Agree

C. Neutral

D. Disagree

E. Strongly disagree

1 or 2 word comments on Lab 3

Refraction (history and modern era):

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 ARTS

dt

d2

ninr

“Ibn Sahl law”𝑑2𝑑𝑡

=𝑛𝑖𝑛𝑡

d

GlassAir

dt

dt

d2

θtθi

“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 veraquantitate (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. Now so-called metamaterials with negative or zero refractive index exist. 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).

What happens if you have nothing? (no light, no particles, no charges, no masses, zero temperature…). Can there be forces?

A. Yes

B. No

Casimir effect (attraction between two metallic plates in vacuum):

Only standing waves possible

Any waves possible (exerts pressure)

figure from Kyle Kingsbury

Casimir effect (attraction between two metallic plates in vacuum due to vacuum fluctuations):

Only standing waves possible

Any waves possible (exerts pressure)

figure from Kyle Kingsbury

Vacuum fluctuations (image from D. Leinweber)

Some consequences of Fresnel equations:

1. Refraction

Augustin Fresnel (source: wiki)

ocw.mit.edu

Fresnel equations visualized

ni

nt

qi qr

qt

Ei

Bi

Er

Br

Et

Bt

Interface

Two cases: (TE and TM) – Transverse Magnetic

and Transverse Electric

ni

nt

qi qr

qt

Bi

Ei

Br

Er

Bt

Et

Interface

TE TM

Electric field is parallel to the interface

(perpendicular to the plane of incidence)

Magnetic field is parallel to the interface

(E field is parallel to plane of incidence)

ni

nt

qi qr

qt

Ei

Bi

Er

Br

Et

Bt

Interface

Two cases: (TE and TM) – Fresnel Equations:

ni

nt

qi qr

qt

Bi

Ei

Br

Er

Bt

Et

Interface

TE TM

𝐸𝑡 = 𝑡𝑇𝑀𝐸𝑖 =2

𝑎 + 𝑏𝐸𝑖

𝐸𝑟 = 𝑟𝑇𝑀𝐸𝑖 =𝑎 − 𝑏

𝑎 + 𝑏𝐸𝑖

𝐸𝑡 = 𝑡𝑇𝐸𝐸𝑖 =2

1 + 𝑎𝑏𝐸𝑖

𝐸𝑟 = 𝑟𝑇𝐸𝐸𝑖 =1 − 𝑎𝑏

1 + 𝑎𝑏𝐸𝑖

𝑎 =cos qtcos qi

𝑏 =𝑛𝑡𝜇𝑖𝑛𝑖𝜇𝑡

Some consequences of Fresnel equations:

1. Refraction2. Total Internal Reflection

Augustin Fresnel (source: wiki)

https://faraday.physics.utoronto.ca/PVB/Harrison/Flash/Optics/Refraction/Refraction.html

ocw.mit.edu

Some consequences of Fresnel equations:

1. Refraction2. Total Internal Reflection3. Multiple reflections

Augustin Fresnel (source: wiki)

8% back reflection

montrealfooddivas.com/independent-montreal-cafes/

Why should sunsets be orange and red?

A. Because the sun emits different colors in the evening

B. Because the atmosphere transmits better red light than blue light

C. Because the atmosphere reflects better red light than blue light

Why should sunsets be orange and red?• The light path at sunset is much longer than at noon when the sun is

directly overhead.

Incident light

Reflected light (R)

Transmitted light (T)

Air Glass Air

R+T=1

r+t=1

tr

incident r+t=1

tr

incident