slides interferometry me657

8/22/2019 Slides Interferometry ME657

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Light waves interfere with each other much like

mechanical waves do.

All interference associated with light waves ariseswhen the electromagnetic fields that constitute

the individual waves combine.

INTERFERENCE

ME-657 Thermal and Fluids Engg.

Laboratory (Atul Srivastava)


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Conditions for Interference

For sustained interference between twosources of light to be observed, there are

two conditions which must be metThe sources must be coherent

They must maintain a constant phase with respectto each other

The waves must have ident ical wavelengths




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Producing Coherent Sources

Light from a monochromatic source is allowed topass through a narrow slit.

The light from the single slit is allowed to fall on a

screen containing two narrow slits.

The first slit is needed to insure the light comesfrom a tiny region of the source which is coherent

Old method.




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Currently, it is much more common to use a laseras a coherent source.

The laser produces anintense, coherent, monochromatic beam over

a width of several millimeters. The laser light can be used to illuminate multiple

slits directly.




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Youngs Double Slit Experiment

Thomas Young first demonstrated

interference in light waves from two sources

in 1801.

Light is incident on a screen with a narrowslit, So.

The light waves emerging from this slit arrive

at a second screen that contains two

narrow, parallel slits, S1 and S2




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Youngs Double Slit Experiment, Diagram

The narrow slits, S1and S2 act assources of waves

The waves

emerging from theslits originate fromthe same wave frontand therefore arealways in phase




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Resulting Interference Pattern

The light from the two slits form a visiblepattern on a screen.

The pattern consists of a series of bright

and dark parallel bands called fringes. Constructive interference occurs where abright fringe appears.

Destructive interference results in a darkfringe.




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Interference Patterns

Constructive

interference occurs at

the center point

The two waves travelthe same distance

Therefore, they arrive

in phase




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Interference Patterns - 2

The upper wave has to

travel farther than the

lower wave

The upper wave travelsone wavelength farther

Therefore, the waves arrive

in phase

A bright fringe occurs




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The upper wave travels

one-half of a wavelength

farther than the lower

wave

The trough of the bottomwave overlaps the crest of

the upper wave

This is destructive

interference

A dark fringe occurs

Interference Patterns - 3




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Interference Equations

The path difference, , is found from the tan

triangle = r2 r1 = d sin

This assumes the paths are parallel

Not exactly parallel, but a very good approximation since L

is much greater than dME-657 Thermal and Fluids Engg.



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For a bright fringe, produced by constructive

interference, the path difference must be either zero orsome integral multiple of the wavelength

= d sin bright = m

m = 0 ,1,2,

m is called theorder number When m = 0, it is the zeroth order maximum

When m = 1, it is called the first order maximum




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When destructive interference occurs, a dark

fringe is observed.

This needs a path difference of an odd half

wavelength.

= d sin dark = ( m + )

m = 0 , 1, 2,




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For bright fringes

For dark fringes

0, 1, 2bright Ly m md

1 0, 1, 22

dark Ly m md

Interference Equations, Final




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INTERFEROMETRY

Consider two point sources, S1 and S2

Electric field vectors associated with each point source can be

described as

).cos(),(11011

wtrkEtrE

).cos(),( 22022 wtrkEtrE

Irradiance at any point P is given by

TEI

2

Time-average of the

magnitude of the electric

field intensity squared.




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Accordingly,

EEE

.2 Where now,

)).(( 21212 EEEEE

And thus,

21

2

2

2

1

2 2 EEEEE




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Now take t ime average of both sides,

1221 IIII Where,

TEI

2

11

TEI 222

TEEI 2112 .2

Interference term




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The interference term is then

cos. 020112 EEI

)( 2121 rkrk

Phase difference arising from a

combined path length and initialphase angle difference.




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The combination of the two waves is Es

)(2cos)(2cos rvtzvtzAEs

Using the identity

2

cos

2

cos2coscos BABA

BA

)2

(2

coscos2 r

vtzr

AEs

Amplitude of the resultant wave

The amplitude depends on the degree to which the two waves are

out-of-phase. ME-657 Thermal and Fluids Engg.Laboratory (Atul Srivastava)


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The irradiance is the square of this amplitude,

rAIs

22

cos4

0,1,2,...where, nnr

Constructive interference

...2

3,2

1

r

Maximum irradiance

Minimum irradiance

Destructive interference(Dark fringes to be formed)




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Change in path length per fringe shift is a constant.

Thetemperature drop per fringe shiftis also aconstant.

Define the function in Equation 1 as :

The fringe temperature on two successive fringes for same value of L can be

given as:

)( 0TTL ),( LTf

dTdn

PL

LTf

),(:1Fringe1

dTdn

PLLTf

),(:2Fringe 2

Temperature drop per fringe shift:

dTdn

LLTfLTf

LT

),(),(1

12




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For example: ForRayleigh Benard Configuration,

Number of fringes in a projection can be estimated directly from the relation:

T

TT coldhot

fringesofNo.



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