Measurements in Fluid Mechanics058:180 (ME:5180)

Time & Location: 2:30P - 3:20P MWF 3315 SC

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Guilichuan-gui@uiowa.edu

Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

2

Lecture 7. Optical experimentation: Nature of light

3

Background for optical experimentation

Light

- radiation that propagates through vacuum in free space,

- in the form of electromagnetic waves,

- wavelength

- both oscillating transversely to the propagation direction

- and normal to each other.

( classical Electromagnetic theory )

- intensities of the electric and magnetic fields oscillate harmonically in time t and along propagation direction x.

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:

4

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

5

Background for optical experimentation

- associated with the orientation of the plane of oscillation of the electric field.

- randomly polarized (unpolarized)

- circularly polarized

∆𝜑=𝜋2

- elliptically polarized

0<∆𝜑<𝜋2

- plane/linear polarized

∆𝜑=0

Polarization

Background for optical experimentation

The colors of light Visible light: wavelength range 380-750 nm

Different types of radiationVisible light colors

Refractive index

c – light speed in vacuum

v – light speed in medium

𝑛=𝑐𝑣

7

Background for optical experimentation

Lorentz-Lorenz (or Clausius-Mosotti) express:

Relationship between refractive index and density

Gladstone-Dale formula - Simplified for gases

22

2

2

1

i

i

e

f

m

L

m

eK

e – charge of an electronme – mass of an electronL – Loschmidt’s numberm – molecular weight – frequency of visualizing lighti – resonant frequency of distorted electron fi – oscillator strength of distorted electron

Kn 1n – refractive indexK – Gladstone-Dale constant – density

In gas mixture of N components:

N

n

nnKK

1

Dependency of refractive index of water on temperature Tc (20-34C) for =632.8 nm:

8

Background for optical experimentation

Light refraction

Law of refraction

Application of refraction: convergent and divergent glass lenses

9

Background for optical experimentation

Light reflection

- glass-air interface: c=42

Law of reflection

Critical angle

Total internal reflection

𝜑1>𝜑𝑐

- glass-waster interface: c=62

10

Background for optical experimentation

Light absorption

Beer’s law:

I – radiant intensity of passing light

I0 – radiant intensity of incident light

– absorption (attenuation) coefficient

l – length of path

Penetration Depth: - a measure of how deep light can penetrate into a material.

- defined at which I=37%I0𝛿𝑝=1𝛼

- small for transparent material- extremely large for opaque material

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

11

Homework

- Questions and Problems: 1 and 2 on page 142

- Read textbook 5.1-5.2 on page 98-107

- Due on 09/10

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image01.bmp A(i,j) for i=1,2,3, M; j=i=1,2,3, N

Start to write a Matlab program• Determine location of maximal gray value i – number of lines

j – number of columns

Clear;A=imread('image01.bmp'); [M N]=size(A);Imax=0;Jmax=0;Gmax=0;for i=1:M for j=1:N if A(i,j)>Gmax Gmax=A(i,j); Imax=i; Jmax=j; end endend[Imax Jmax Gmax]

>> MatlabProgram

ans =

17 11 255

MatlabProgram.m