Geometric OpticsGeometric Optics

1.1. consider only speed and direction of a rayconsider only speed and direction of a ray2.2. take laws of reflection and refraction as factstake laws of reflection and refraction as facts3.3. all dimensions in problems are >> all dimensions in problems are >>

What can happen to a beam of light when it hits What can happen to a beam of light when it hits a boundary between two media?a boundary between two media?

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, , Addison-Wesley, Reading, MA, 1998.Reading, MA, 1998.

Conservation LawConservation Law

= 1= 1

= Fraction Absorbed= Fraction Absorbed

= Fraction Reflected= Fraction Reflected

TT = Fraction Transmitted = Fraction Transmitted

TransmissionTransmission

How is light transmitted through a medium such How is light transmitted through a medium such as glass, Has glass, H22O, etc.?O, etc.?

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Rayleigh ScatteringRayleigh Scattering

•Elastic (Elastic ( does not change) does not change)

•Random direction of emissionRandom direction of emission

•Little energy lossLittle energy loss

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-, Addison-Wesley, Reading, MA, 1998.Wesley, Reading, MA, 1998.

Spherical WaveletsSpherical Wavelets

Every unobstructed point of a wavefront, at a given instant, Every unobstructed point of a wavefront, at a given instant, serves as a source of spherical secondary wavelets. The serves as a source of spherical secondary wavelets. The amplitude of the optical field at any point beyond is the amplitude of the optical field at any point beyond is the superposition of all these wavelets.superposition of all these wavelets.

What happens to the rays What happens to the rays scattered laterally?scattered laterally?

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, , Addison-Wesley, Reading, MA, 1998.Reading, MA, 1998.

Are you getting the concept?Are you getting the concept?

Why are sunsets orange and red?Why are sunsets orange and red?

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Forward PropagationForward Propagation

Wavelets constructively Wavelets constructively interfere in the forward interfere in the forward direction.direction.

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, , Addison-Wesley, Reading, MA, 1998.Reading, MA, 1998.

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Scattering is Fast but not Infinitely FastScattering is Fast but not Infinitely Fast

What effect does this have on the phase of the wave?What effect does this have on the phase of the wave?

If the secondary wave lags, then If the secondary wave lags, then phase of the resultant wave also lags.phase of the resultant wave also lags.

If the secondary wave leads, then If the secondary wave leads, then phase of the resultant wave also phase of the resultant wave also leads.leads.

velocity > cvelocity > c

velocity < cvelocity < c

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, , Addison-Wesley, Reading, MA, 1998.Reading, MA, 1998.

New velocity can be related to cNew velocity can be related to cusing the refractive index (using the refractive index ())

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

v

c v

c

is wavelength and is wavelength and temperature dependenttemperature dependent

In glass In glass increases as increases as decreasesdecreases

What about the energy in the wave?What about the energy in the wave?

Remember: E = hRemember: E = h

Frequency remains the sameFrequency remains the sameVelocity and wavelength changeVelocity and wavelength change

Douglas A. Skoog and James J. Leary, Principles of Instrumental Douglas A. Skoog and James J. Leary, Principles of Instrumental Analysis, Saunders College Publishing, Fort Worth, 1992.Analysis, Saunders College Publishing, Fort Worth, 1992.

Refraction is a consequence of velocity changeRefraction is a consequence of velocity change

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Snell’s Law ofSnell’s Law of RefractionRefraction

Wavefront travels BD in time tWavefront travels BD in time t

Wavefront travels AE in time tWavefront travels AE in time t

BD = vBD = v11tt

AE = vAE = v22tt

21 v

AE

v

BD

21 v

AE

v

BD

1

cADsin1

2

cADsin2

1

cADsin1

2

cADsin2

11sinsin11 = = 22sinsin22

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Are you getting the concept?Are you getting the concept?

Light in a medium with a refractive index of 1.2 strikes aLight in a medium with a refractive index of 1.2 strikes amedium with a refractive index of 2.0 at an angle of 30medium with a refractive index of 2.0 at an angle of 30degrees to the normal. What is the angle of refraction degrees to the normal. What is the angle of refraction (measured from the normal)? Sketch a picture of this(measured from the normal)? Sketch a picture of thissituation.situation.

ReflectionReflection

v and v and do not change do not change

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, , Addison-Wesley, Reading, MA, 1998.Reading, MA, 1998.

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Law of Specular ReflectionLaw of Specular Reflection

Velocity is constantVelocity is constant

=> AC = BD=> AC = BD

AD

BD sin 1 AD

BD sin 1

AD

AC sin 3 AD

AC sin 3

ADsinADsin33 = ADsin = ADsin11

33 = = 11

Angle of Incidence = Angle of Reflection

Fresnel EquationsFresnel Equations

For monochromatic light hitting a flat surface at 90For monochromatic light hitting a flat surface at 90ºº

Important in determining reflective losses in optical Important in determining reflective losses in optical systemssystems

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

at different interfacesat different interfaces

Reflective losses quickly become significantReflective losses quickly become significant

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Antireflective CoatingsAntireflective Coatings

Melles Griot CatalogueMelles Griot Catalogue

= 1= 1 = 1.38= 1.38 = 1.5= 1.5

= 0.025

= 0.002

Total Total = 2.7% = 2.7%compared to compared to (() = 4.0% ) = 4.0%

without coatingwithout coating

Melles Griot CatalogueMelles Griot Catalogue

Film thickness further reduces reflectionsFilm thickness further reduces reflections

Melles Griot CatalogueMelles Griot Catalogue

Observed Observed for MgF for MgF22 coated optic coated optic

If incident beam is not at 90If incident beam is not at 90ºº use Fresnel’s use Fresnel’s complete equationcomplete equation

componentcomponent componentcomponent

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

For an air-glass interfaceFor an air-glass interface

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

For unpolarized light, For unpolarized light, increases increases as as 11 increases increases

componentcomponent componentcomponent

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.

Example of highExample of high at high at high 11

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Brewster’s AngleBrewster’s Angle

11 where where of polarized light of polarized light

is zerois zero

1

21-p tan

1

21-p tan

For an air-glass transition For an air-glass transition pp

= 58= 58° ° 40’40’

Are you getting the concept?Are you getting the concept?

Suppose light in a quartz crystal (n = 1.55) strikes a boundarySuppose light in a quartz crystal (n = 1.55) strikes a boundarywith air (n = 1.00) at a 50-degree angle to the normal. At whatwith air (n = 1.00) at a 50-degree angle to the normal. At whatangle does the light emerge?angle does the light emerge?

Why?

Ingle and Crouch, Ingle and Crouch, Spectrochemical AnalysisSpectrochemical Analysis

Total Internal ReflectionTotal Internal Reflection

11sinsin11 = = 22sinsin22

Snell’s Law:Snell’s Law:

If If 22 = 90 = 90ºº

1

21-c1 sin

1

21-c1 sin

At any At any 11 cc T( T() ) 0 0

For a glass-air transition For a glass-air transition cc = 42 = 42ºº

Eugene Hecht, Eugene Hecht, OpticsOptics, Addison-Wesley, Reading, MA, 1998., Addison-Wesley, Reading, MA, 1998.