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Measurements in Fluid Mechanics
058:180:001 (ME:5180:0001)
Time & Location: 2:30P - 3:20P MWF 218 MLH
Office Hours: 4:00P – 5:00P MWF 223B-5 HL
Instructor: Lichuan Gui
[email protected]
http://lcgui.net
Lecture 7. Optical experimentation: Nature of light
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Background for optical experimentation
Light ( classical Electromagnetic theory )
- radiation that propagates through vacuum in free space,
- in the form of electromagnetic waves,
- both oscillating transversely to the propagation direction
- and normal to each other.
- intensities of the electric and magnetic fields oscillate
harmonically in time t and along propagation direction x.
 - wavelength
T – period of oscillation
- frequency of oscillation:  =1/T
- wave number: =1/
- phase speed:  = /T = 
- speed of light propagation in vacuum: c = 2.998  108  300,000 km/s
- relation between amplitudes of electric and magnetic fields:
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Background for optical experimentation
Wave front
- a surface with constant phase in electric/magnetic filed.
- plane wave: all wave fronts are plane
- spherical wave
- cylindrical wave
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Background for optical experimentation
Polarization - associated with the orientation of the plane of oscillation of the electric field.
- plane/linear polarized
- elliptically polarized
∆𝜑 = 0
- randomly polarized (unpolarized)
0 < ∆𝜑 <
𝜋
2
- circularly polarized
∆𝜑 =
𝜋
2
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Background for optical experimentation
The colors of light
Visible light: wavelength range 380-750 nm
Visible light colors
Refractive index
𝑐
𝑛=
𝑣
c – light speed in vacuum
v – light speed in medium
Different types of radiation
Background for optical experimentation
Relationship between refractive index and density
Lorentz-Lorenz (or Clausius-Mosotti) express:
Gladstone-Dale formula - Simplified for gases
n 1  K
n – refractive index
K – Gladstone-Dale constant
 – density
1 e2 L
fi
K

2 me m  i2   2
e – charge of an electron
me – mass of an electron
L – Loschmidt’s number
m – molecular weight
 – frequency of visualizing light
i – resonant frequency of distorted electron
fi – oscillator strength of distorted electron
N
In gas mixture of N components:
K   Kn
n 1
n

Dependency of refractive index of water on temperature Tc (20-34C) for =632.8 nm:
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Background for optical experimentation
Light refraction
Law of refraction
Application of refraction: convergent and divergent glass lenses
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Background for optical experimentation
Light reflection
Law of reflection
Critical angle
Total internal reflection
𝜑1 > 𝜑𝑐
- glass-air interface: c=42
- glass-waster interface: c=62
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Background for optical experimentation
Light absorption
I0 – radiant intensity of incident light
I – radiant intensity of passing light
l – length of path
 – absorption (attenuation) coefficient
- extremely large for opaque material
- small for transparent material
Beer’s law:
Penetration Depth: - a measure of how deep light can penetrate into a material.
𝛿𝑝 =
1
𝛼
- defined at which I=37%I0
Birefringence (double refraction)
decomposition of a ray of light into two rays when it
passes through certain anisotropic materials, such as
crystals of calcite or boron nitride.
- unequal indices of refraction in two directions
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Homework
- Read textbook 5.1-5.2 on page 98-107
- Questions and Problems: 1 and 2 on page 142
- Due on 09/09
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