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