Fermat’s Principle Kathy Geise April 2007

Slides:

Advertisements

Similar presentations

Ch 9 Earth and Space By R. Aldridge. sun the star at the center of our solar system.

Advertisements

Geometrical Optics for 1 st year Physics Honours Course By Arnab Gangopadhyay.

Agenda: Here comes the sun April 10 1.Learning Target: I can make a presentation of one aspect of solar study to teach other astronomers about the sun.

Chapter 23: Fresnel equations Chapter 23: Fresnel equations

Refraction n 1 = 1 n 2 > 1 11 22 1 2 Radius = vT = (c/n)T 11 22.

Chapter 35 Serway & Jewett 6th Ed..

Lecture 15 Ray Optics Chapter 23 PHYSICS 270 Dennis Papadopoulos March 9, 2010.

Solar and Lunar Eclipses! What causes Solar and Lunar Eclipses?

Refraction   Refraction   When light bends as it passes from one material to another due to a change in speed Optical illusions 9/13/2015APHY1011.

Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London.

1 Huygens’ and Fermat’s principles (Hecht 4.4, 4.5) Application to reflection & refraction at an interface Monday Sept. 9, 2002.

Chapter 2: Geometrical optics

What’s seismology about?

Example problem 1 Example problem 2

Laws of Optics. Why study the Laws of Optics Extra Practice with Pythagorean Theorem Practice with d=rt relationship Study Domain and Range Mathematical.

Review for Test #1  Responsible for: - Chapters 35 and 36 and section Notes from class - Problems worked in class - Homework assignments  Test.

Eclipses. Two Types – Solar Eclipse – Lunar Eclipse Solar Eclipse – The moon blocks the earth’s view of the sun. Lunar Eclipse – The earth blocks the.

Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London.

Polarization. When a plane EM wave incident at an oblique angle on a dielectric interface, there are two cases to be considered: incident electric field.

Sun – Most important star to us on Earth. The sun and all of the heavenly bodies that orbit it make up our solar system.

Maxwell’s Equations Differential forms electromagnetic waves y x z E ⊥ B, and E ⊥ k, B ⊥ k, k is the direction of the wave. Polarization of electromagnetic.

Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London.

Eclipses. Solar Eclipse A solar eclipse happens when the moon blocks the light from the Sun from reaching the Earth People who live in the umbra of the.

The Sun Youra Taroyan. Age 4.5 ×10 9 years Mean diameter 1.392×10 6 km, 109 × Earth Mass ×10 30 kg, 333,000 × Earth Volume 1.412×10 18 km 3, 1,300,000.

Sources (EM waves) 1.

Solar and lunar Eclipses. Eclipses The Sun and Moon occasionally line up so that we have an eclipse. –These eclipses happen every year –To see a solar.

Eclipses. What are eclipses? When the shadow of one CELESTIAL body falls on another.

Refraction Chapter 12 (p ). Refraction Refraction: The bending or change in direction of light when it travels at an angle from one medium into.

Formation of the Rainbow Logan Bonecutter April 24, 2015.

Guiding Questions for Objective 5 & 6 What are the important parts of a ray diagram? What is the purpose of drawing a ray diagram? How is a ray diagram.

Eclipses. Shadows Note the shadow differences with a small light source vs. a large light source.

Chapter 25 Reflection and Refraction. Reflection.

Air Liquid A question based on refractive index, Snell’s law, total internal reflection, and some geometry.

Solar and Lunar Eclipses!

Solar Eclipses Solar Eclipses.

Polarization of Electromagnetic Waves

Chapter 24 Geometric Optics

Refraction of Light.

EM spherical waves …in any coord. system

Solar Eclipses Solar Eclipses.

Wave Physics PHYS 2023 Tim Freegarde.

“Ray Optics: Reflection, Refraction, Polarization”

Sources (EM waves) 1.

Tools of Astronomy.

The Sun: Portrait of a G2V star

The Moon and Earth.

Reflection and Refraction (Snell’s Law).

Refraction Changing of speed of a wave (light) when it travels from one medium to another. When light travels from one medium into another at an angle,

Eclipses Two types of eclipses.

The Sun Chapter 17.

Star Light Star Bright Desktop Constellations

Medium: material through which electromagnetic waves (e. g

Refraction and Reflection

PRISMS – one of the e.g. of optical instrumentation

Natural Optics KM Geise Ampère’s Law.

Fluid Equations Continuity Equation Euler Equation Energy Equation.

Geometrical Optics (Chapter 2)

Interactive applet: Fun with Snell’s Law.

Inquiry (home tasks) By Juliet.

Quantum Optics and Least Action

REVISION REFRACTION.

Question of the Day: Which path should a lifeguard (L) take at a

SHADOWS Are formed when an opaque object is placed in front of the path of light.

The Index of Refraction

Lights, Camera, Action! Slide Show Assessment.

Light wave is coming out of page

Aim: How do we explain Snell’s Law?

OPTICAL FIBRES.

Presentation transcript:

Fermat’s Principle Kathy Geise April 2007 Optics Fermat’s Principle Kathy Geise April 2007

Fermat’s Principle

Fermat’s principle When a light ray travels between any two points, its path is one that requires the least time. n2>n1

Fermat’s principle Take the derivative of t with respect to x and set the derivative equal to zero.

Fermat’s principle

Snell’s Law of refraction Fermat’s principle Snell’s Law of refraction

Fermat’s Last Theorem xn+yn=zn Andrew Wiles http://video.google.com/videoplay?docid=-4898647796750952274&q=fermat%27s+last+theorem http://www.pbs.org/wgbh/nova/proof/

Credits The cover photo is a picture of a solar flare in the Sun’s chromosphere recorded by Japan’s Hinode spacecraft on January 12, 2007. The magnetic vortex is roughly the size of the Earth. Resolution is 0.2-arc seconds. http://science.nasa.gov/headlines/y2007/21mar_chromosphere.htm Chromosphere photographed during solar eclipse.