Transcript Ch. 35

Chapter 35
Serway & Jewett 6th Ed.
How to View Light
As a Ray
As a Wave
As a Particle
What happens to a plane wave passing through an aperture?
Point Source
Generates spherical
Waves
The limit of geometric (ray) optics, valid for lenses, mirrors, etc.
y
{ }
Eo cos (kx - t)
Bo
E
x
B
z
Surface of constant phase
For fixed t, when kx = constant
Index of Refraction

n
o
medium 
vac
n
1 n1 = 2 n2
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 Refraction
in the limit of Ray Optics
1. Huygens’s Principle
2. Fermat’s Principle
3. Electromagnetic Wave Boundary
Conditions
Huygens’s Principle
Huygens’s Principle
All points on a wave front act as new sources
for the production of spherical secondary waves
k
Fig 35-17a, p.1108
Reflection According
to Huygens
Incoming ray
Outgoing ray
Side-Side-Side
AA’C   ADC
1 = 1’
Refraction
Fig 35-19, p.1109
Show via Huygens’s Principle Snell’s Law
v1 = c in medium n1=1
and
v2 = c/n2 in medium n2 > 1.
Fundamental Rules for
Reflection and Refraction
in the limit of Ray Optics
 Huygens’s Principle
2. Fermat’s Principle
3. Electromagnetic Wave Boundary
Conditions
Fermat’s Principle and Reflection
A light ray traveling from one fixed point to another will follow
a path such that the time required is an extreme point – either a
maximum or a minimum.
Fig 35-31, p.1115
Rules for Reflection and Refraction
n1 sin 1 = n2 sin 2
Snell’s Law
Optical Path Length (OPL)
n=1
n>1
L
L
vac

vac
n
P
S
P
OPL   n( x)dx
S
When n constant, OPL = n  geometric length.
For n = 1.5,
OPL is
50% larger
than L
Fermat’s Principle, Revisited
A ray of light in going from point S to point P
will 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 Refraction
in the limit of Ray Optics
 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