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.TH‘S

ADAFTTON OF THE QUARTZ
SDECTROGRAPH
T0 PRECISION MEASUREMENT OF LENGTH

THESIS mp. THE DEGREE 01? M. 3.

Harold Warner Edwards
' 1930

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ADAPTI ON OF TEE QUARTZ SPEC TROGRAPH
TO

PRECISICN MEASURHJENT OF LENGZH

Thesia‘ for Degree of M. 8.
Harold Warner Edwards

1930

I wish to express 11w sincere appreciation and
gratitude to Dr. G. W. Chamberlain under whose super-
vision this thesis was made possible. I also wish to
extend w thanks to Professor 0. W. Chem for his
kind cooperation, and to Professor W. E. Leycock for

his help in the photographic work.

H. '27. Edwards.

105523

The object of this thesis is to show how a large
quarts speotograph of the auto-collimating type, refer-
1113 particularly to the 'Littrow" may be used in con-
Junction with an interferometer to make and record
precision measurements to the fraction of a light wave.
As an illustration, this thesis will describe in detail

a measurement of the Radius of Molecular Attraction.

TABLE 93; oozrmzos

Introduction
Detailed description of the Littrow Spectrograph

Visual methods of measurement, using the mall
spectroscOpe and the interferometer
The use of the large spectroscope compared with
the smaller type
Method of setting up the refraction and interference
system with the Littrow Spectrograph
Description of interferometer
Measurement of transparent objects
Measurement of opaque objects
Adjustment of interferometer
Position of spectrograph and interferometer
Description of path followed by the light
Photographic record and its interpretation
Mathematical development of fomulae
General formula
Special formula used in this thesis
Measurement of the Radius of Molecular Attraction
Brief review of work on Radius of Molecular Attraction
Early work by Newton,Johonott and others
Mapsis of Dr. Chamberlain's work at Columbia

Measurement of a silver film

Preparing the film

Method of measurement

Data

Calculation of the Radius of Molecular Attraction
Conclusion

Bibliography

THE LITTROW'SPECTROGRAPH

fibers are a great.many types of spectroscoPes and
spectrographs in use today. Many of these are designed
for a particular purpose, while others have been designed
to increase the dispersion and at the same time extend
into the ultra-violet, which necessitates photography.
As the resolving power and the dispersion of the ordi-
nary 60 degree prism type spectroscope is increased it is
necessary to increase the length of the collimator and
telesc0pe tubes. These may be increased to the point
where they become cumbersome and unsteady. This
limitation brought about the auto collimating type of
spectrosc0pe of which the Littrow is the most important.
In the auto collimating type the same lens and optical
path are used for both the collimator and the telescope--
thus shortening the instrument by one-half.

In the Littrow spectograph the light enters the slit
on the side of the case. The slit is equipped with a'
diaphram and micrometer adjustment graduated to .01 of a
Imillimeter. From the slit the light passes into a small
total reflecting prism. The light diverges from the slit,

covers the face of the small prism, and by the time it

.1.-

reaches the lens has diverged sufficiently to cover the
entire face of the lens. The light now passes through the
lens and enters the 50 degree quartz prism which is faced on
the rear with tin amalgam, reflecting the light back
through the prism, through the lens and is focused on the
photographic plate. Plate No. 1 shows this path of the
light. Consider in this description that the inter-
ferometer is the source of light.

The refracting face of the prism is approximately
98 x 57 mm and subtends an angle of 30 degrees. The light
passes through the prism twice, giving it the effect of a
60 degree prism. In the usual 60 degree prism of quartz,
the quartz must be half of the right handed and half of the
left handed type. In the Auto-collimating'type of spectro-
graph the prism need be of only the right handed type. Only
one lens is needed in this type of spectrograph and this
need be of only one variety of quartz. The prism is not
placed exactly perpendicular to the path of light from the
lens, but is tilted slightly in order that the light may
pass over the totally reflecting prism and reach the
photographic plate. The lens is of right handed quartz
and has a clear aperture of 70 mm. and a focal length

of 1700 mm. The instrument is capable of photographing

-2-

wave lengths from 2100 to 8000 Angstroms units. This range
must be taken at three separate exposures. For each ex-
posure the lens and the prism are brought into focus and
the prism rotated automatically by a hand wheel on the
outside of the case. There are very delicate adjustments
on the lens, prism and the totally reflecting prism so
that in case the instrument is not brought into adjust-
ment automtically each part may be adjusted separately.
The plate holder is capable of being moved up and down so
that it is possible to obtain as many as 10 exposures on
the same plate with the proper slit height. A plate is
furnished by the Cramer Dry Plate Company, that is
sensitive to wave lengths shorter than the red. The
plate is very thin in order that it may be pressed to the
curvature of the plate holder. The plate used measures
2 5-4" x 10". The actual measurement will be explained

later in this report.

use pg THE mmrmormraa fl PRECISION W

For many years light waves have been used in mking
precision measurements, but until recently it was a tedious
and delicate undertaking to make a measuremnt using light

waves. Professor Michelson has designed several types of

interferometers which will measure a distance in terms of
the wave length of light. In the laboratory sodium light
is usualky used.

As this interferometer is used in conjunction with
the spectroscope to make measurements by the method de-
scribed in this thesis it is described here. First, as
the name implies, the interferometer makes use of the
interference of light. Due to the fact that light waves
are so short and their frequency so high, the only way
that they can be caused to interfere is to separate a
beam of light into two paths, then cause it to reunite in
such a manner that it sdll interfere. That is, if one of
the separated beams does not travel an Optical path,
identical with the other beam, the two beams will interfere
on being brought together. The interfermmeter is an
instrument for controlling the conditions of interference.

Light first comes to the instrument and meets a
parallel plate of glass at a 45 degree angle, passes
through the glass to a half silvered film on the rear of
the glass plate. A half silver film.means that half of
the light passes through the film and the other half is
reflected. This is how the instrument separates a beam
of light into two paths. The two beams leave the plate

at right angles to each other. They each travel a

certain distance from the plate to a totally reflecting
mirror and are reflected back on themselves to the silver
film. Here the light is again united though only half of
the light leaves the instrument in such a manner that it
can be seen, the other half travels back toward the

source. If the parallel plates and.the end.mirrcrs are

all perpendicular to the same plane and the end mirrors

at a 90 degree angle to each other, the wave fronts sent
out by these mirrors will be parallel. (See interferometer
part of plate No. 1). If one of the mirrors is placed on a
loving carriage it may be moved very accurately and
parallel to itself. The paths between the two beams can be
changed by a fraction of a wave length. If the two paths
differ in length by half a wave of any particular wave
length, or any odd number of half wave lengths there will
be interference and this particular wave length will not

be able to pass through the instrument. In case the two
end mirrors are not parallel a series of vertical parallel
lines will show in the field; if the mirrors are parallel
however, circles will be seen. These circles are to the
eye only, due to the curvature of’the eye. They are
really plane parallel waves. The interferometer alone has

been used to make measurements, by using a more or less

-5-

monocromatic source of known wave length and counting the
bands as they travel across the field of view with a move-
‘ment of the end mirror, each band representing a movement
of the mirror of half a wave length of the light used..

In this thesis we are interested in what happens to
the interfering wave fronts when an incandescent source is
used. we have previously shown that an interferometer will
cause interference with any wave length entering the
instrument, provided the distance between the two mirrors
varies by an odd.multip1e of half wave lengths of that
light. With an incandescent source, which means a con-
tinuous spectrum, the interferometer will cause interference
with all wave lengths that are odd number of half wave
lengths difference in path between the two mirrors. Thus
if we had a method of analysing the light leaving the
interferometer we would find a spectrum, that was originally
continuous, but now is missing in certain wave lengths.

9g; 93; m SPECTOGRAPH in; PRECISION mammgg

The spectroscOpe is an instrument that will analyze

this light. Placing a spectroscope in front of the inter-
ferometer will cause vertical dark bands to appear where the

wave lengths are missing. Now as one of the mirrors is

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essag _t_g count the bands while the mirror EMM°
The bands need only be counted before and after the measure-
ment is made. The method of calculating the measurements
will be described later in this report.

For the visual work the smaller spectroscmpes are
used. Small spectroscOpes permit dissembling and placing
the interference system between the collimtor and the prism.
This makes the instrument more compact and the adjustment
more simple. ‘

The Littrcw spectrograph is of the autca-collimating
type as are most of the larger SpectroscAOpes, which means
that the same lens and optical path are used for both the
collimator and the telescope, making any separation im-
possible. The interference system must therefore be set up
outside of the spectrograph. This thesis describes a
method of setting up the refracting and interfering systems
and the adjustments necessary for photographing. For

high precision work a very stable interferometer must be

chosen, and one with very delicate adjustments for bringing

-7-

the end mdrrors into parallelism, and a very accurate bed
for carrying the moving mirror, together with a very accu-
rate micrometer screw for shifting the moving carriage. A
Fabry and Perot interferometer with a Michelson attachment
was used in this thesis. This attachment was constructed
by shaping a flat piece of brass to carry the two station-
ary parallel plates. This plate was secured to the instru-
ment by two screws on the stationary part of the head. One
of the end mirrors was fastened to a small brass plate and
mounted on the adjustable beam that carried the Fabry and
Perot mirror. The beam referred to is approximately 3/8"
square by 4" long, made of steel. On one end of this beam
is fastened very rigidly, the instrument. On the mirror
end there are two adjustments, one vertical and the other
horizontal. These adjustments consist of two screws each:
one screw working inside the other. One screw has thirty-
six right hand threads per inch and the other screw has 34
left hand threads per inch. Thus in thirty-six turns of
the outside screw the inside screw actually moves only two
threads. These screws press against the extreme end of the
beam referred to above. The other mirror is fastened to
the platform which carried the Fabry and Perot moving

mirror. It is possible to see how the and mirrors and the

two parallel-plates are placed on the interferometer by
referring to plate No.2 of this thesis.

For measuring transparent objects, no more interfer-
ometer equipment is necessary. The device for holding the
substance to be measured, must either be placed on the bed
of the interferometer or supported on a stand separate from
the interferometer. Two readings must be taken without any
change in the interferometer adjustment. One reading without
the substance in the field and the other with the substance
in the field of light. From the difference in the number
of bands between the two readings, the thickness of the
substance in question may be calculated. A precaution is
necessary in placing any substance directly across the field
that might reflect light, as this reflection would cause
dimming of the bands. Any light entering the slit that has
not come from the and mirrors, will not be in a condition to
cause interference. To avoid this error the inserted plates
are placed at an angle, Just sufficient to throw all reflected
light from their faces off the slit. Precauticn should also
be taken to keep the inserted plates at the same angle dur-
ing a measurement. Any shift in this angle changes the
length of that cptical path. Any glass container of sub-

stances to be measured, must have optically plane surfaces

-9.-

at points, through which the light passes. Compensator
plates or glasses must be placed in the other path of light,
so as to keep the optical paths equal.

Measurement of Opaque objects, necessitates setting
up the interferometer in such a manner, that the mirror may
be moved the exact thickness of the object to be measured.
One illustration of how this is accomplished, is to move
the carriage against a fixed stop, make a reading, withdraw
the carriage and insert the object to be measured against
this stop and again draw up the carriage, taking another
reading. Some provision must be made in order that the
pressure between the fixed stop and the carriage is always
constant. This is done by the use of weights.

The interferometer is now ready for use, and may be
adjusted in the ordinary manner with the use of the sodium
flame; adjusting the end mirrors to parallelism, and
equalising the paths between them. If any plates are to be
inserted during the measurement they should be inserted
at this point and the final adjustment made with them in
place. The interferometer may now be placed in position,
as is shown in plate No.1 with reference to the spectre-
graph. The lens collimating light from the source should

be adjusted to give slightly diverging light. Light must

~10-

enter the interferometer and slit directby.

Plate NO. 1 traces the path of light from the source
to the photographic plate. If the interferometer is in
adjustment, vertical dark bands should appear in the spectrum
as soon as one of the optical paths is increased. The
appearance of these bands in the spectrum does not necessar-
ily indicate that the interferometer is in adjustment.
Though the bands appear dark to the eye, they are not void
of all light unless the interferometer is in perfect adjust-
ment, and if there is any light present in the dark bands,
the photograph will be too blurred to obtain an accurate
measurement.

Final adjustment of the interferometer for photograph-
ing, can best be made by viewing the spectrum with a lens or
ground glass, and changing one of the cptical paths in such
direction that the bands move from the red to the blue. As
soon as the bands become very wide and are few in number,
they will commence to curve and finally turn over and appear
to come into the field from the Opposite direction. At the
point where the bands changed direction, the optical paths
of the interferometer were equal, and white light fringes
should be formed on a screen of white paper placed over the
slit. If the fringes on the screen are in the form of bands
the interferometer is out of adjustment, and one of the end

mirrors should be adjusted in such a manner that the screen

.11..

appears to be illuminated with one color only, as this is
a true indication that the interferometer is in perfect
adjustment. A very slight movement of one of the mirrors
should cause the screen to be illuminated with first one
color, then another down through the spectrum. Further
change in one Of the Optical paths will place enough bands
in the field to photograph distinctly.

A tungsten band filament is a convenient source of
light. The filament carries 16 amperes at 6 volts.’ A
slit width of .2 mm and an orpOsure of two minutes will
make a good photograph. Bands thus formed will measure the
difference in Optical paths between the two mirrors to an
accuracy of (lO)-7cms. Reference lines of some known
spectrum may be superimposed on the bands to locate the
wave lengths.

To make a measurement, it is necessary to take a
photograph Of the bands, without the Object to be measured
in the field of light, than without any change in the
interferometer adjustment, place the object to be measured
in one of the optical paths and re-photograph. Place the
reference lines over the bands, and by means of the formula
developed later in this thesis, compute the change in the

Optical path. From the index Of refraction of the substance

.1 2...

measured, this figure may be changed into distance.

MATMIATIQAZQ DEVELOPMENT _O_F_ FOEMAE

The condition for interference in the interferometer
is that twice the difference in path between the two mirrors
equals (n+5-)L: n being any integer. If the interferometer
is placed in front of the spectrograph, bands will occur
where the above equation is satisfied. From the super-
imposed helium spectrum, the wave lengths of two lines
uddely separated are known and the number of bands between
the positions of these two wave lengths are recorded in
the photograph. The problem is to interpret in terms of
centimeters the increase in cptical path corresponding to
the addition of one band in that portion of the spectrum
included between the two spectral lines, whose wave lengths
are known.

Let L1 and L2 be the heliummwave lengths between
which the number of bands are counted. Change the optical paths

so as to add one band between L1 and L2.

Let the number of bands passing L1 - x
n n n n n l!’ .1
L2 +1
Since the product of the number of bands passing a certain

wave length and that wave length in cms. is a constant, the

.13-

increase in cptical path is
XI.1-'(x-rl)1..2
Whence
x-L L-L
2/( 1 2)

It is to be noted that x is the number of bands passing L1

Eberefore the change in cptical path

-XL1-L1Lz/(L1-Lz)

-14-

Several different methods have been employed to
leasure the Radius of Molecular attraction. Leidenfrost, in
1756, measured the greatest diameter to which it was
possible to inflate a soap bubble with a known quantity of
soap. Plateau found the thickness of a liquid which
reflected the pale yellow of the first order of Newton's
rings. Drude, in 1891, considered the effect of a
capillary on the reflection and refraction of light. The
black spot on liquid films, was first discovered by
Newton: its thickness was measured by Reinold and Rucker
and found to be 1.2 (10).gms. By Bakker's method this
gives .2 (10)-7cms. for the Radius of Molecular attraction.

There being a great discrepancy between various direct
and indirect methods of the measurement, Dr. Chamberlain,
in 1910 undertook a series of experiments, trying to locate
these errors. Dr. Chamberlain used several methods of
measurement, one of which involved the use of very thin
silver wedges. These wedges may be formed in several
different ways. One way is to place two interferometer
plates together, then insert a thin glass rod between
them on one edge. Two wedges were formed at a time, of

equal thickness. These two wedges, thus formed, were

placed V93? 01°39 together to form a capillary, ‘

.15-

and set in water. The attraction between silver and water
being zero, the point at which the water ceases to climb in
the capillary is theoreticalhy the distance through which
glass acts on water. The height to which the water raised
in the wedge was measured with a cathetometer. Dr.
Chamberlain measured the thickness of the silver film at
this point and obtained a result of 2.7 (10)-60ms. with a
correSponding figure of 1.5(10)-7cms. for the Radius of
Molecular Attraction. The measurements were made by the
use of the compound interferometer, an instrument designed
by Dr. Chamberlain. Dr. Chamberlain also made extensive
measurements on the thickness of black.spots on liquid films.
msmmm _0_1‘: THE RADIUS gig MOLECULAR ATTRACTION
by the
REFRACTION AND INTERFERENCE.METHOD

In this thesis the silver films were deposited from
silver solution. By prOperly timing and testing several
films it was possible to cover half of an interferometer
plate with an even film which would Just prevent the
attraction of the glass for the water. Several films were
measured that were both thicker and thinner than the final
film. Only results of the final film will be given here.

The silvering solution used was the standard solutions used

-15-

in the Rochelle Salts Process. The silvering solution,
wash.water, and plates were kept at nearly the same
temperature during the silvering process. The silver be-
ing opaque, a few crystals of iodide were very carefully
moved over the surface of the silver, changing the silver
to silver iodide, which is transparent.

Having prepared the silver iodide film, the next step
was to make a very accurate measurement of its thickness,
using the process described above. The film.to be measured
covered half of an interferometer plate belonging to a pair.
The mate to the plate containing the film, was placed in
the path of the immovable mirror, the angle of the plate
was measured by its reflection on the slit. The plate
was placed at an angle Just sufficient to keep all the
reflection from its faces, off the slit. The plate
containing the film was placed on a hardwood block out at
a height which would bring the plate in the optical path
when placed on top of the block. The block rested on the
bed of the interferometer. The angle of this plate was
determined by matching the reflections of the other plate
on a screen placed over the slit. Then as it was very
essential that this angle did not change during the

measurement, two guide pins were driven into the block

-17-

supporting the plate. The plate was replaced on the block
and crowded against the guide pins with the clear part in
the optical path. With the two plates in position, the
interferometer was set up and adjusted for circular white
light fringes, by the use of the sodium flame. The
interferometer was then placed in front of the spectrograph
and lined up with the slit and source of light. With a

I tungsten band filament lamp carrying 16 amperes at six
volts, and preperly shielded to keep all stray light out
of the room, the and mirrors were brought to accurate
parallelism by use of the screen over the slit. The
screen was removed and 10 to 15 bands brought into the
field by changing one of the optical paths. With a

slit width of .2 mm and an eXposure of two minutes, a
photograph of the bands in the field was taken. The plate
containing the film was carefully moved so that the film
was in the path of light. Great care was taken not to
touch the carriage of the interferometer or either of the
and mirrors. Vibration was reduced to a minimum during the
entire measurement. A photograph was taken with the film
in the optical path, giving a three minute exposure to
allow for poor transparency of the film. Again the plate
was shifted with the clear glass in the path and re-
photographed, This was done to obtain a check on the
stability of the set-up. All three of the above photos

were taken very close together on the same plate by raising
the plate. With a full height slit a helium spectrum was
placed over all three eXposures to locate the reference
lines necessary to the measurements.

By the use of a comparator, which reads accurately
to a thousandth of a millimeter, the number of bands and
fraction of bands were counted between two reference lines
of helium. The following table gives the readings as
they were taken from the comparator on the final plate.
Under high magnification the bands were too far apart to
read the center accurately, so the beginning and the end
cf each band was read and the center computed. This
makes a very accurate method of counting fractions of bands.
A band was read on both sides of the limiting helium line,
thus making it possible to definitely locate the inter-

section of the bands and the helium lines.

.19..

TABLE

 

 

 

Helium Film Glass _
gggegin End Center Begin End Center

86.994 85.984 86.489 88.741 86.645 87.693

85.000 84.257 83.018 83.138 85.260 84.025 84.593
82.134 81.095 81.615

80.907 80.840 79.945 80.393 79.042 78.279 78.659
77.405 76.693 77.049 75.855 75.227 75.541

73.995 73.443 73.719 72.849 72.212 72.530

70.949 70.745 70.136 70.441 69.736 69.244 69.390
67.415 66.897 67.157 66.574 66.023 66.298

64.118 63.479 63.807 63.521 63.000 63.260

60.787 60.174 60.461 60.360 59.690 60.025

58.546 57.273 56.715 56.999 56.970 56.434 56.702
54.090 53.540 53.815 53.860 53.301 53.580

52.394 50.884 50.220 -50.552 50.662 50.070 50.366

 

The Helium lines chosen for reference points, were

located according to the table, at 85.000 and 52.394 milli-

meters, which have a wave length of 4950 and 4370 angstroms

respectively. Substituting in the formula developed in

-20-

this thesis under Mathematical Calculations:

4950 x 4370
Change in optical path per band change - - _ — _
4950 - 437

 

' .0000373 cms.
Computing from the table, the number of bands between
the two helium lines, with the film in the Optical path
I10.918
Number of bands for clear glass - 11.514. Band shift ' .533
Since one band represents a change in optical path of .0000373cms.
.533 x .0000373 - .00001988 cms.
' .00002 cms. approximately.
.00002/2 - cptical thickness of silver iodide
' .00001 cms.

To change the thickness of silver iodide to silver:

Chemical equivalent of silver, Ag '107.9
" " of silver iodide, A31.“ 234.9

Density of silver iodide, d1 '5.602
" " " , d2 - 10.55

Index of refraction of silver iodide,n1 . 2.246
RElation between the thickness of silver D and silver iodide E
is as follows:
1 2
D-Ag/Angd/d xE-.2439E

.6
Thus 000001 1e2439 .2e43 (10L 01118.

~21-

CONCLUSION

The thickness of the silvered film as measured above
was 2.43 (IN-Gems. Applying the correction omitted by
Quincke, and published by Dr. Chamberlain, the Radius of
Molecular Attraction as determined by the combined Quartz
Spectcgraph and Interferometer, was found to be 1.4 (10).7‘cms:
one four hundredth of a yellow light wave. As the limit of
a perfect compound microsc0pe is 1/2 of a light wave, the
measurement recorded above is 200 times beyond the limit of

the microscOpe.

-22-

1.

2.

3.

4.

5.

6.

7.

BIBLIOGRAPHY

Spectroscopy by 2.0.0. Baly Vol. 1.
The Littrow Spectrograph
Physical Optics - Lamb
The Michelson interferometer
A Treatise on Light - Houstoun
Interference of Light
The'Use of'Light waves in Precision Measurements
Thesis for M.S. Degree by S.H. Deight
PhilosOphical Transactions 1881 701.11 Page 447
"Electrical Methods of Determining the
Magnitude of the Radius of Molecular
Attraction"
Philosophical Transactions 1886 Vol. 11 Page 627
"Relation between thickness and surface
tension of liquids - Reinold and Rucker
Physical Review - Vol. 1 1910 Page 170
Radius ofiholecular Attraction -

Dr. C. W. Chamberlain

-23-

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MICHIGQN STQTE UNIV. LIBRQRIES

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