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Geometric Optics
1. consider only speed and direction of a ray
2. take laws of reflection and refraction as facts
3. all dimensions in problems are >>
What can happen to a beam of light when it hits
a boundary between two media?
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Eugene Hecht, Optics, Addison-Wesley,
Reading, MA, 1998.
Conservation Law
() + () + () = 1
() = Fraction Absorbed
() = Fraction Reflected
T() = Fraction Transmitted
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Transmission
How is light transmitted through a medium such
as glass, H2O, etc.?
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Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Rayleigh Scattering
Elastic ( does not change)
Random direction of emission
Little energy loss
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Eugene Hecht, Optics, Addison-
Wesley, Reading, MA, 1998.
Spherical Wavelets
Every unobstructed point of a wavefront, at a given instant,
serves as a source of spherical secondary wavelets. The
amplitude of the optical field at any point beyond is the
superposition of all these wavelets.
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What happens to the raysscattered laterally?
Eugene Hecht, Optics, Addison-Wesley,
Reading, MA, 1998.
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Are you getting the concept?
Why are sunsets orange and red?
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Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Forward Propagation
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Wavelets constructivelyinterfere in the forward
direction.
Eugene Hecht, Optics, Addison-Wesley,
Reading, MA, 1998.
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Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Scattering is Fast but not Infinitely Fast
What effect does this have on the phase of the wave?
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If the secondary wave lags, then
phase of the resultant wave also lags.
If the secondary wave leads, then
phase of the resultant wave also
leads.
velocity > c
velocity < c
Eugene Hecht, Optics, Addison-Wesley,
Reading, MA, 1998.
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New velocity can be related to c
using the refractive index ()
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
v
c=
is wavelength andtemperature dependent
In glass increases as
decreases
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What about the energy in the wave?
Remember: E = h
Frequency remains the same
Velocity and wavelength change
Douglas A. Skoog and James J. Leary, Principles of InstrumentalAnalysis, Saunders College Publishing, Fort Worth, 1992.
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Refraction is a consequence of velocity change
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
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Snells Law of Refraction
Wavefront travels BD in time t
Wavefront travels AE in time t
BD = v1t
AE = v2t
21 v
AE
v
BD=
1
cADsin
1
=
2
cADsin
2
1sin1 = 2sin2
Ingle and Crouch, Spectrochemical Analysis
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Are you getting the concept?
Light in a medium with a refractive index of 1.2 strikes a
medium with a refractive index of 2.0 at an angle of 30degrees to the normal. What is the angle of refraction
(measured from the normal)? Sketch a picture of this
situation.
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Reflection
v and do not change
Eugene Hecht, Optics, Addison-Wesley,
Reading, MA, 1998.
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Ingle and Crouch, Spectrochemical Analysis
Law of Specular Reflection
Velocity is constant
=> AC = BD
AD
BDsin 1=
AD
ACsin 3=
ADsin3 = ADsin1
3 = 1
Angle of Incidence = Angle of Reflection
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Fresnel Equations
For monochromatic light hitting a flat surface at 90
Important in determining reflective losses in optical
systems
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Ingle and Crouch, Spectrochemical Analysis
() at different interfaces
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Reflective losses quickly become significant
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
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Antireflective Coatings
Melles Griot Catalogue
= 1 = 1.38 = 1.5
() = 0.025
() = 0.002
Total () = 2.7%
compared to () = 4.0%
without coating
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Melles Griot Catalogue
Film thickness further reduces reflections
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Melles Griot Catalogue
Observed () for MgF2 coated optic
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If incident beam is not at 90 use Fresnels
complete equation
component component
Ingle and Crouch, Spectrochemical Analysis
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For an air-glass interface
Ingle and Crouch, Spectrochemical Analysis
For unpolarized light, () increases
as 1 increases
component component
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Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Example of high
() at high 1
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Ingle and Crouch, Spectrochemical Analysis
Brewsters Angle
1 where () of polarized lightis zero
=
1
21-p tan
For an air-glass transition p= 58 40
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Are you getting the concept?
Suppose light in a quartz crystal (n = 1.55) strikes a boundary
with air (n = 1.00) at a 50-degree angle to the normal. At whatangle does the light emerge?
Why?
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Ingle and Crouch, Spectrochemical Analysis
Total Internal Reflection
1sin1 = 2sin2
Snells Law:
If 2
= 90
==1
21-c1 sin
At any 1 c T() 0
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For a glass-air transition c = 42
Eugene Hecht Optics Addison-Wesley Reading MA 1998