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Measurement of Coefficient of Linear Expansion by Fizeau's Method. Objective

This document describes an experiment to determine the coefficient of linear expansion of aluminum using Fizeau's interferometer method. Key steps included: 1. Measuring the fringe width in an interference pattern produced by the interferometer at different temperatures as the aluminum rod expanded. 2. Calculating the coefficient of linear expansion from the change in fringe width over the temperature change using the formula provided. 3. The measured coefficient was 9.43 × 10-6 rad/C with an estimated error of 0.929 × 10-6 rad/C.

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Gaurav Kumar Tiwari
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660 views4 pages

Measurement of Coefficient of Linear Expansion by Fizeau's Method. Objective

This document describes an experiment to determine the coefficient of linear expansion of aluminum using Fizeau's interferometer method. Key steps included: 1. Measuring the fringe width in an interference pattern produced by the interferometer at different temperatures as the aluminum rod expanded. 2. Calculating the coefficient of linear expansion from the change in fringe width over the temperature change using the formula provided. 3. The measured coefficient was 9.43 × 10-6 rad/C with an estimated error of 0.929 × 10-6 rad/C.

Uploaded by

Gaurav Kumar Tiwari
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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28/10/2010

Gaurav Kumar Tiwari


Y0911016

Exp. no-8
Measurement of Coefficient of linear expansion
by Fizeau’s method.

Objective
To determine the coefficient of linear expansion of Aluminium by Fizeau inter-
ferometer configuration.

Apparatus
• Specimen is Aluminium rod to measure the coefficient of thermal expan-
sion.
• Two glass plates is used to reflect the light ray from each of them to obtain
the interference pattern
• Thermocouple and temperature indicator to measure the temp. the rod
is at.
• Travelling microscope is used to measure the fringe width at each temp.
• Variable transformer to vary the power supply.
• Sodium vapour lamp as light source .
• Heater is to heat the rod.

1 Theory
The basic theory is to calculate the fringe width in different temp. As the temp
rises the rod expands and there will be a change in the width of the fringe.
We’ll note the distance between two dark fringes by noting the condition for
dark fringe for two waves from the two glass plates formed due to interference.
For dark fringe condition:
λ λ
(2m + 1) = 2t1 + (1)
2 2
0.0572
λ λ
(2(m + 1) + 1) = 2t2 + (2)
2 2

1
For finding fringe width. eq2 - eq1

2(t2 − t1 ) = λ (3)
t2 and t1 are distance between the two glass plates at (m+1) and m dark
fringe. ¿From geometry

(t2 − t1 ) = βtan(θ) (4)


β is the horizontal distance between (m+1) and m dark fringe. And θ is the
angle between two glass plates. ¿From the above two eqns.
λ
θ = tan− ( ) (5)
2β
Coefficient of linear expansion is given by

∆L = LRT α∆T

And ∆L = l∆θ. Sub all.


l∆θ
α= (6)
LRT ∆T
Where ∆θ = tan− ( 2βλn ) − tan− ( 2βn−1
λ
)

Observations
Room temp. = 30o C
LRT = 20.2mm
length of glass plate = 54mm
No. of fringe = 25
Wavelength = 589nm

Temp(C) No. of fringe fringe width(cm)

35 25 0.0572
45 25 0.0564
57 25 0.0542
67 25 0.0518
73 25 0.0504
80 25 0.0502
83 25 0.0499

Table 1: Calculating fringe width

2
fringe width(cm) tan− ( 2β
λ
) δ tan − λ
( 2β ) height

0.0572 0.001029524 0.000071944


0.0564 0.001044858 0.000074103
0.0542 0.001087269 0.000080241
0.0518 0.001137644 0.000087849
0.0504 0.001169245 0.000092797
0.0502 0.001173904 0.000093538
0.0499 0.001179543 0.000094439

Table 2: Calculating Coefficient of thermal expansion

0.0013
’plot2’ u 1:2:3:4
y(x)

0.00125

0.0012

0.00115
Theta

0.0011

0.00105

0.001

0.00095
30 40 50 60 70 80 90
Temp.(degree)

Figure 1: Calculating slope

slope= 3.4 × 10−6 rad/C


α = 9.43 × 10−6 rad/C (From Graph)

3
Error Analysis
Calculating Error in Coefficient of thermal expansion
∆α (from graph) = 0.929 × 10−6 rad/C

Result
α = (9.43+0.929) × 10−6 rad/C (From Graph)

Precautions & Discussions


• Do not touch the heater or rod by hand when oven is on.

• Be careful while handling the glass plates.


• The major default in the experiment is the measurement of temp. which
isn’t stable and fluctuates.
• Morever, we aren’t sure about the exact temp. of the rod.

• I did the practical taking distance between 30 fringe in every temp.


• For error analysis, population sampling was done.
• The quantity to determine is of minute value, the vigilance throughout
the experiment is important.

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