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Chapter 35Serway & Jewett 6th Ed.
How to View LightHow to View Light
As a ParticleAs a Particle
As a RayAs a Ray As a WaveAs a Wave
The limit of geometric (ray) optics, valid for lenses, mirrors, etc.
What happens to a plane wave passing through an aperture?
Point SourceGenerates spherical
Waves
Surface of constant phaseFor fixed t, when kx = constant
B
E
x
y
z
cos (kx - t){ }Eo
Bo
1 n1 = 2 n21 n1 = 2 n2
Index of Refraction
o
n
nvac
medium
When material absorbs light at a particular frequency,the index of refraction can become smaller than 1!
When material absorbs light at a particular frequency,the index of refraction can become smaller than 1!
Reflection and Refraction
Oct. 18, 2004
Fundamental Rules for Reflection and Refractionin the limit of Ray Optics
Fundamental Rules for Reflection and Refractionin the limit of Ray Optics
1. Huygens’s Principle
2. Fermat’s Principle
3. Electromagnetic Wave Boundary Conditions
1. Huygens’s Principle
2. Fermat’s Principle
3. Electromagnetic Wave Boundary Conditions
Huygens’s PrincipleHuygens’s Principle
Fig 35-17a, p.1108
Huygens’s PrincipleHuygens’s Principle
All points on a wave front act as new sources for the production of spherical secondary waves
All points on a wave front act as new sources for the production of spherical secondary waves
k
Reflection According to Huygens
Reflection According to Huygens
Side-Side-SideAA’C ADC
1 = 1’
Side-Side-SideAA’C ADC
1 = 1’
Incoming ray Outgoing ray
Refraction
Fig 35-19, p.1109
v1 = c in medium n1=1 and
v2 = c/n2 in medium n2 > 1.
Show via Huygens’s Principle Snell’s Law
Fundamental Rules for Reflection and Refractionin the limit of Ray Optics
Fundamental Rules for Reflection and Refractionin the limit of Ray Optics
Huygens’s Principle
2. Fermat’s Principle
3. Electromagnetic Wave Boundary Conditions
Huygens’s Principle
2. Fermat’s Principle
3. Electromagnetic Wave Boundary Conditions
Fermat’s Principle and ReflectionFermat’s Principle and Reflection
A light ray traveling from one fixed point to another will followa path such that the time required is an extreme point – either amaximum or a minimum.
Fig 35-31, p.1115
n1 sin 1 = n2 sin 2
Snell’s Law
n1 sin 1 = n2 sin 2
Snell’s Law
Rules for Reflection and RefractionRules for Reflection and Refraction
Optical Path Length (OPL)
When n constant, OPL = n geometric length.
nvac vac
LLn > 1n = 1
For n = 1.5, OPL is
50% larger than L
For n = 1.5, OPL is
50% larger than L
P
SdxxnOPL )(
S P
Fermat’s Principle, Revisited
A ray of light in going from point S to point Pwill travel an optical path (OPL) that minimizes the OPL. That is, it is stationary with respect to variations in the OPL.
Fundamental Rules for Reflection and Refractionin the limit of Ray Optics
Fundamental Rules for Reflection and Refractionin the limit of Ray Optics
Huygens’s Principle Fermat’s Principle
3. Electromagnetic Wave Boundary Conditions
Huygens’s Principle Fermat’s Principle
3. Electromagnetic Wave Boundary Conditions
ki = (ki,x,ki,y) kr = (kr,x,kr,y) kt = (kt,x,kt,y)
Fig 35-22, p.1110
Fig 35-25, p.1111
Fig 35-24, p.1110
Fig 35-23, p.1110
Total Internal Reflection
Slide 56 Fig 35-27, p.1113
Total Internal
Reflection
p.1114
p.1114
Fig 35-30, p.1114
Fig 35-29, p.1114