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.g A NEW METHOD FOR MEASURING

‘fi THE REFLECTING POWER .

1 OF RETROREFLECTORS
Thesisfor the Degree of M‘ S.

1. MICHIGAN STATE COLLEGE

i HarryC. Morgan

g 1939

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DATE DUE DATE DUE DATE DUE

 

 

A.NEWWMETHQD FOR MEASURING
THE REFLECTING POWER OF

RETROREFLEDTORS

BY

HARRY CLARK MOI-KEN

A THESIS

Summitted in partial fulfilment of the requirements
for the degree of Master of Science in the
Graduate School, Michigan State College

Department of Physics
East Lansing, Michimn
June 1939

Acknowle damsnt

 

I wish to express my sincere appreciation to
Dr. C. I. Chamberlain of the Physics Department of
Michigan State College for his invaluable
assistance and encouragement. I am.also indebted
to Mr. Robert L. Bows for his advice and aid in the
photographic phase of this thesis. The ready advice
and interest of the Physics Department staff has

made my task a pleasant one.

9642/7ng

12141.88

Table of Contents

Article

Statement of Prdblem

Theory of the cats eye retroreflector

Theory of central triple retroreflectors

Methods of measurement

Method and measurement of Reflected Cone

Description and Theory of Apparatus

Measurement of the Efficiency of Retroreflectors at
Different.Angles of Incidence I

Efficiency of cats eye reflectors for different angles
of incidence

The efficiency of central triple retroreflectors for
different angles of incidence

Photographs of Reflector Patterns at Different angles
of Incidence

Design of Itnproved Apparatus

Page

15

18

20

27

29

35

43

50

Page 1

Statement of Problem

The need for lighting aids of some form to increase safety on our
highways is recognized by all drivers. Modern headlights when switched
to illuminate the road far ahead do fairly well for speeds under fifty

miles per hour. The higher speeds, at which a large percentage of us
are wont to drive, often bring us upon curves and hazards before our
muscles have time to obey the comands of the brain. Approaching cars
with their bright lights cut down our visibility to a mall fraction
of what it was previously. Iith a constant stream of oncoming traffic
we do well to know Just where the side of the road is. A good night
driver is one who does not worry ever the possibility of a man who has
become negligent walking on the edge of the pavement.

One safety aid, which is in dispute at the present time, is the
illumination of our Iain highways by overhead electric lights every
thousand feet or so. his might be a great aid but for its high cost
of installation and nightly consumption of power. Scone” dictates
that the lights be spaced as far apart as possible. This results in
regions of relative darkness succeeded by regions of bright light.

[it high speeds this rapid fluctuation of intensity strains the eyes,
especially the irises which are forced to expand and to contract, and
rapidly fatigues the driver.

These facts night well be kept in wind throughout the discussion
of the retroreflector which may engineers are enthusiastically
investigating.

The retrorefleetor is a surprising device. It utilizes the light

Page 8

of the headlights of the oncaning car, and reflects it back to the
driver's eyes so that it appears like a small electric light beside
the road far ahead. The light may strike the reflector at widely
varying angles of incidence and still, be reflected back in the
direction from which it cane.

Devices using this principle have been developed in the past ten
years by several comercial companies and have been widely used in
read signs to indicate curves, cross roads, railroads, and other
hazards of the road. We have come to expect thn to urn us of
approaching danger. lords are spelled out with letters formed with
several “cats eye retroreflectors‘.

A more recent type which shows great prcnise has as its funda-
mental unit three planes which meet at right angles to each other,
or might be termed a cube corner. This reflector was devised by
Augustin J’. Fresnel, a famous French scientist of the early nineteenth
century. Incident light is also reflected back upon itself to the
driver's eyes by reflectors comprising a plurality of cube corners.
This typO of reflector has been used to outline the road between
Lansing and Detroit as a test installation. The Nichimn State
Highway department reports that since the installation, night
accidents have been reduced forty percent. lly personal observations
have convinced as that these reflectors have nude travel much safer.
The road is clearly outlined far ahead, and obstacles, web as
parked cars and pedestrians blot out one or more of the reflectors
thus showing their presence.

It would be interesting at this point to discuss seas of the

properties of a good retroreflector. Obvipusly it must return light

 

which falls upon it at different angles of incidence with the axis of
the reflector. The button must not return the light directly back to
its source, but in a cone of about one degree so that part of the
reflected light enters the driver's eyes. This angle represents a
practical compromise and gives the driver a brightly illuminated
reflector at distances ranging from two or three thousand feet to
about a hundred feet frm the car to the reflector.‘ lhen an angle
of about forty degrees is made by the incident light and the axis of
the reflector, the car is close to the retroreflector. The reflector -
need not return: light at greater anglers."I

The reflecting surface of the retroreflector should not deter-
iorate with time. Deterioration of the reflecting powers of a
reflector would require frequent replacement and thus added cost and
an increased road hazard if the poor units are not imadiately
replaced.

Very little work has been published on mthods of measurement
of the optical properties of retroreflectors. Accurate measurements
of the efficiency of retroreflectors at different angles of incidence
as well as quality of workmenship is very desirable. aich measurements
enable the higiway engineer to determine the merit of various
retroreflectors and to select those retrcreflectors which will best
serve the driving public. The information derived from these
measurements will indicate what further research and improvement is
necessary.
‘ R. Kingslake an apparatus for testing highway sign reflector units.

Journal of the Optical Society of America Vol. 28,
”to 1938 pas. 323s

Theory of the cats eye retroreflector

Figure l diagramatically represents the simple theory of the cats
eye retroreflector. IA.converging lens brings parallel light to a
focus. Light ray 1 is bent so as to approach the normal line to the
lens. lhen it reaches the focus at point B, ray 1 undergoes reflection
at an angle which is twice the angle between the incident ray at B
and the normal to B and the lens. The reflected ray enters the lens
at l'and emerges frmm.the lens parallel to the entrant path, but
displaced. Ray 2 makes an angle with the normal to the lens, is
refracted by the lens and is brought to the lens focus at point A
where it undergoes reflection. The reflected ray makes an angle with
the incident ray of twice the angle that the incident ray'mskes with
the normal to a. This reflected ray is refracted by the lens at
point I. so that it emerges parallel to but displaced from the entrant
path. Surface AB must therefore coincide with the focal plane of
the lens and also have the normal at every point in its surface pass
through the center 0 of the lens.

Figure 2 shows an early type. The system consists of the major
portion of a glass sphere and.a metal reflector a short distance
behind the glass.

figure 3 shows a.more recent type incorporating several improve-
ments. The focus of the lens is at the rear surface of the lens.
Silver is used to make this surface reflect the light back through the
lens. This silver coat is protected by a heavy coat of lacquer or
paint. This type secures retrorefleotion at much greater angles of

incidence than the type shown in figure 2.

Page 5

The neximnm.angle of incidence with the lens axis is determined
by the physical limitations imposed by the design. Theoretically a
cats eye could be made which would retroreflect at ninety degrees
incidence with the lens. However as stated on page three retrore-
flection is not necessary at such e great angle. ‘As has been shown,
the reflected light must not return perfectly upon its incident path
but in a small cone which includes the driver's eyes. It is difficult
to design a reflector which will accomplish this. The lens is cast
and as a result does not have optical surfaces. Light incident at
anglel‘with the lens axis is distorted and the returned light forms

different kinds of patterns.

 

 

 

 

     

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Figure 2 Figure 3
Early type of Improved retroreflector

retroreflector

Page 7

Theory of central triple retroreflectors

The theory of the Fresnel facet may be more easily understood if
we consider the simpler two dimensional case before the three dimen-
sional case.

Figure four shows two reflectors, AB and B0 at right angles to
each other. A light ray I is incident at F making an angle 1 with
the normal 3]? and a complementary angle y with BC. By the law of
reflection the ray DP makes the same angle 1 with the normal E! and
the same complementary angle y with BF. Ray BI is incident at D,
making an angle y' with the normal m and a complementary angle 1'
with AB. The reflected ray R by the law of reflectibn makes the
same angle y' with the normal m and the same complementary angle
1' with AB. lines the sum of the inside angles of a triangle equals
180 degrees, it is obvious that x' 4- y + 90 s 180 degrees or that
x’ + y e 90 degrees and 1' + y' I 90 degrees. ED is perpendicular
to LB, and E? is perpendicular to BC. AB was constructed perpendicu-
lar to DC. D]! is thereby parallel to BC. Since y' 3 y, the reflected
ray R is parallel to the incident ray 1, but displaced, for any angle
of incidence x. I

A much simpler proof which will be used in the three dimensional
case is as follows. ' The lines 8'0, 0'1), 1", I"! represent extensions
of the original lines shown. Since the included angles formed by two
intersecting lines are equal, 1' a x" a x'" a x and y' s y" s y'" s y.
It'can be seen that the incident ray I upon reflection at I is rotated

through an angle of y I} y or 2y degrees. Ray ID is again reflected
and rotated thrmghban angle of x + x or 81 degrees from its incident

A path. Ii'he ray R has thus been rotated through a total angle of

 

Figure 4

Page 9

8:-+ 2y or 180 degrees (since I + y s 90 degrees) upon the double
reflection. The ray R is thus parallel to ray I but reversed in
direction.

Figure five illustrates the three dimensional case of retrore-
flection. It is plainly seen that the addition of one more dimension
canplicates the geometry of the problem. PG, JB, AN, are nonnals to
the points of incidence of the light ray. lProjections of the light
ray onto yz planes are: BO onto B6, AB onto BB. Projections of
light rays onto :2 planes are: IO onto 00, GB onto EC, CB onto BF,
AB onto H, AB onto BK, AB projected down onto EH, RA onto PA, BA
onto GB; It is not necessary to prove that angles are equal as on.
page 7, it will be assumed that their equality is obvious. The method
used just preceeding this discussion will now be resorted to.

The incident ray I is rotated through an angle 2w in the plane
determined by BECDI, but zero degrees in the plane 12. Ray BO incident
at B is reflected along,AB. By virtue of the projection of AB onto
Bfl'and of B0 onto BG ray B0 is rotated through an angle of 20. By
virtue of the projection of BC onto EC and ofvdB onto EH ray B0 is
rotated through an angle of 2w. Ray BA incident on point A is reflec-
ted along RA. The ray BA is rotated zero degrees in the y direction
in which it is measured. Ray BA is rotated through an angle of 2u
as shown by the projections. Swaming the angular rotations we find:

w + w +20 - 180 degrees by the fact that w +0 : 90 degrees and that
.‘Lu + v + v a 180 degrees by the fact that u + v = 90 degrees. The
reflected ray RA is thus parallel to the incident ray 10 but

reversed in direction.

 

 

 

Figure 5

Page ll

One of the first central triple retroreflector: was made up of
triangular'faces forming the cube corners aslshown in figures six,
seven and eight. This reflector however is not very efficient. By
ovserving the reflection of an enlarged facet with parallel light
incident upon it one finds the corners as shown by figure 7 with
the lines ABC, DEF, GHI dark. This means that some of the light
which falls upon the facet leaks out the side after two reflections
and is lost. This amounts to about thirty per cent loss. At twenty
five degrees incidence with the axes of the retroreflector, only
the region JGMK is illuminated. Thus niarIY’two thirds of the
incident light is lost. This is a very interesting experiment and
should be carried further. The comercial reflectoerade up of these
facets have about one hundred units joined edge to edge in the form
of a disk.

An improved design is a facet composed of three square surfaces
meeting at right angles. This concave facet is shown in figure 9.
At axial incidence the reflector turns all the light which falls upon
it. This does not take into consideration the light which is lost
because of imperfect internal reflection. ,At about forty degrees
incidence, as shown by figure ten, the point B is turned outwardly,
and the bottom.in, relative to the paper. The only portion of the

mirror which is filled with reflected light is the area IBGB, making

about twenty five percent reflection. The rest of the incident
light is lost out the sides after one or two reflections. Figure
eleven shows the same reflector rotated thirty degrees in the
opposite direction. The region ABCDEF, about thirty five percent of

the surface, is filled with reflected light. These results were

 

 

Figure 6

 

 

 

 

 

Figure 7 Figure 8

Normal Incidence 25O Incidence

Page 13

obtained with facets made with silvered mirrors viewed through a half
silvered mirror held at forty five degrees between facet and the
observer. The parallel light enters the system.from the side and is
reflected from.the half silvered mirror.

Commercial retroreflectors are composed of about a hundred cube
corners as illustrated in figure eleven. The front face of the
reflector is somewhat convex, and the back face is composed of the cube
corners. The reflection of light is dependent upon total reflection
from the cube faces. .More specifically, the light is incident upon
the cube faces in the transparent media of the reflector at angles
greater than the critical angle. If light is incident upon a cube
face at less than the critical angle, that light is lost.

The preceding theory is of necessity brief. In the near future,
Dr. 0. w. Chamberlain, of this department, will publish a complete

theory of the central triple retroreflector. He will also discuss

mathematically the efficiency of the reflectors.

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Page 15

Methods of Measurement

There have been several laboratory methods devised to test
retroreflectors. The standard test adopted in 1932 in the joint
I.E.S-S.A.E. Standard Specification for laboratory Tests of Reflex
Reflectors for Motor Vehicles is a visual one. The reflector under
test is placed one hundred feet from.a ten thousand candle power
headlight thus furnishing an illumination of one foot candle at the
reflector. The apparent candle power of the reflector is compared
visually by an observer who is looking at the reflection with his
eyes seven inches above the head lamp. With an illuminated opal glass
screen placed beside the button the intensity of the light placed
behind the screen can be varied at will.‘

A.more accurate measuring device was made by' R. Kingslake,
University of Rochester, Rochester, New York. Figure twelve is a
simple sketch of his method. L.is the lamp house, 8 asbestos screens,
0 the condensing lens, R the photovoltaic cell, D the diaphragm, M
the microammeter, T the objective lens, and B the reflector under test.

The principle of.Mr. Kingslake's apparatus is as follows. The
hole in the photovoltaic cell permits light to emerge via the con-
densing lens as a point source. The lens T refracts the light so that
it is parallel when incident upon the button being tested. The button
reflects back through the lens T to the point source in the center of
the photovoltaic cell (the hole) and causes no meter deflection. If
the reflector returns the light in.a small cone, the light in the

cone causes a meter deflection. The diaphragm.limits the size of the

cone to any size desired. The meter deflections are assumed to give

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Page 17

an indication of the efficiency of the button as a retroreflector

for highway use.’

’ Apparatus for Testing Highway Sign Reflectors by R. Kingslake,
Journal of the Optical Society of America Vol 28 prt. 1938

Page 18

Method and Measurement of Reflected Gone

I am indebted to Dr. C. I. Chamberlain for this excellent method.
Figure thirteen illustrates the arrangement of apparatus. P is
parallel light from a heliostat arranged so as to bring parallel
sunlight into the laboratory. H is a half silvered mirror at forty
five degrees incidence with the sunlight, R is the retroreflector
under examination, and‘d is a white paper screen. Two times the
angle x, shown in figure 13, is equal to the angle of the apex of

the cone.

 

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Page 19

Table I
S was found to be 21 feet, 5% inches. Light was normal to reflector.

Central Triple Retroreflectors

Reflector d D 2x
green 1 5/8 in 4.5 in 42'
white 1 s/s in 7 in 1°1s'

amber (same as green reflector)

Cats eye retroreflectors

Reflector d D 2x
green ‘A 13/16 in. s in so'
green B (too faint to be measured)

green 0 13/16 in 2 in 16'

The green and amber central triple retroreflectors are designed
for the rear of trucks. Therefore the small cone would probably be
satisfactory. The white one, which is like the reflectors between
Lansing and Detroit appears to be correct. The cats eye cones seem

rather small.

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Page 20

Description and Theory of Apparatus

Figure fourteen illustrates the apparatus used. L is a six to
eight volt thirty-two candle power auto headlamp budb. M.is a
collimating lens of about seven inches focal length. 0 is the
rotating block on which the button being tested is fastened. P
is a scale calibrated in degrees, and 0 the pointer. H , H.are half
aluminized mirrors. 3 is a Heston Photronic photovoltaic cell. K.is
a triple pole, double throw knife switch. G is a very sensitive
galvanometer. A is a zero to ten ammeter. V is a zero to fifteen
volts voltmeter. R is a variable resistor. S is a single pole single
throw knife switch. D is a diaphragm with the same aperhture as the
reflector.

Assume that the mirrors have fifty percent films. Fifty percent
of the light is transmitted by the first mirror, and fifty percent of
the transmitted light is reflected by the second mirror, twenty-five
percent is incident upon the photoelectric cell. The fifty percent
of the light incident upon the first mirror is reflected to the
button being tested. If the button reflects one hundred percent of the
light, the fifty percent is reflected back to the first mirror where
half of the fifty percent or twenty-five percent is transmitted to the
photoelectric cell which is moved to receive it. If the retroreflector
being tested does not reflect all of the incident light, the photo-
electric cell will have a decreased current output which when compared
with the current generated by the light reflected from.mirror number

two is a measure of the reflecting power of the retroreflector. The

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Page 22

mirrors need not be fifty percent reflectors and transmitters, nor
he alike, just so long as the actual reflecting and transmitting
power is known for each film.

The switch I was inserted so that the photoelectric cell could
be disconnected and at the same time so that the gayanometer could
be short-circuited to make it dead heat.

The most difficult part of the apparatus to construct is the
fifty percent mirrors. The mirrors were silvered a great many times,
but a satisfactory fifty percent film which was the same for each

mirror could not be produced. The evaporation of aluminum in a
vacuum onto the mirrors was then tried. The second attempt was
successful. By visual test the films were judged to be about eighty
percent reflecting. These mirrors were used in the apparatus. After

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the data, which‘Ts\recorded in this paper~was.completed, the film
thickness was tested by interrupting a beam of parallel light which
fell upon the photoelectric cell with the mirrors and noting the
difference in galvanometer reading. The results obtained were these:
one mirror transmitted 2.4% of the incident light, the other 1.69%.
This indicates the unreliability of visual tests on.mirror trans-
mitting and reflecting powers. The standard visual test of standing
between two lights of the same intensity and viewing the one through
the mirror and the other by reflection from the mirror is thus shown
to be unreliable.

A photovoltaic cell was selected because the apparatus will
eventually be taken out on the road to make tests on reflectors which
are in service. It also eliminates the need for'a high voltage

direct current battery for the photocell. Since the manufacturer did

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not furnish curves which showed the relationship between the
intensity of incident light and the current generated by the photo-
electric cell, data gigwtaken to determine this relationship. The
current changes as the cell is placed at different distances from a

standard electric light bulb on an optical bench. This data‘lsx‘

listed in table II and istlotted on graph I.

Page 24

Table II

Sburce 6-8 volt auto bulb standardized as 5.82 Candle power

current I d in meters l/d2 light intensity
of Galv.. from light in.meter candles
1.3 1.5 .444 2.58
1.5 1.4 .458 2.67
1.7 1.3 .592 3.44
1.98 1.2 .694 4.04
2.38 1.1 .827 4.81
2.90 1.0 1.000 5.82
3.62 .9 1.234 7.18
4.40 .8 1.56 9.08
5.78 .7 2.20 12.80
7.85 .6 2.776 13.24
11.45 .5 4.00 23.25
13.70 .45 4.94 28.75
16.80 .4 6.25 36.35
18.57 .375 7.11 41.30
21.68 .35 8.16 47.45

Theoretically the output current of a photovoltaic cell doubles
when the illumination is twice as great. For low light intensities
and a low external resistance in the cell circuit this is true.

Graph one shows that this is true to‘within a few percent. lhen the
illumination exceeded 35 meter canhles the distance between the

light source and the cell was too small for the inverse square law to
be applied. The variation of cell output for the same illumination

will be discussed later.

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Page 26

After a few experiments, it became evident that alternating
current could not be used to power the lamps in the apparatus. The
line voltage fluctuations made consistent readings impossible.
Storage batteries were then resorted to with excellent results. All
measurements have been made with this source of direct current

energizing the light bulbs.

Page 27

Measurement of the Efficiency of Retroreflectors

at Different.Angles of Incidence

The procedure has already been outlined in brief. A more
detailed explanation is in order at this point. The light is kept
at constant brilliancy by proper manipulation of the variable
register R in figure fourteen. The reflector is secured to block C.
The photocell is then illuminated with the light passing through
diaphragm D. The galvanometer deflection is noted. The photo-
electric cell is then moved over so that the reflected light from
the retroreflector is incident upon its surface. The galvanometer
deflection is noted. The angle of incidence of the light on the
reflector is now changed and the galvanometer deflection is noted.
After the retroreflector is explored at all desired angles of
incidence, a check is made upon the light emerging from the diaphragm
D. The galvanometer was usually shorted and the photocell dis-
connected by throwing switch K over to the left. This protected the
galvanometer from damage by large currents when the lights were
turned on to change the angle of incidence. It often appeared to
make the data more consistent since the cell had time to recover
between readings.

It was now necessary to calculate the correction factor needed
to compensate for the differences in transmission and reflection
percentages of the two mirrors.

The mirror which transmits 1.69fi of the incident light was
placed in the position of Bland thelnirror which transmits 2.4% was

placed in the position of IE in figure fourteen. One way to determine

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Page 28

the correction is illustrated as follows:

looz'mirror

 

 

.985

amount of incident
light :1

 

.02l Transmitted
.976 Reflected

.0169 Transmitte
.985 Reflected

.985x.0169 3.0156 ”b.0169x.9'76 2.0165
which'is the fraction of which is the fraction
the original light ‘ of the original light
incident on incident on photocell
photocell
:0136 = 1.007 Hence the calculated % for a

100% mirror is too high by .7%.

Therefore all calculated percentages of reflection will be high by
.T$. To correct a calculated percentage, multiply the calculated
percentage by .T% and divide by 100. Then add this result to the

calculated percentage.

.

Page 29

Efficiency of cats eye reflectors for different angles of incidence.

Auto bulb operating at 8 volts, 3.86 amps.

Table III

green reflector A

Angle of Galv. deflec- Amount

incidence Galv. tion if 100% reflected

in degrees deflection efficient in %
90 right e1 5e4 0
40 e1 0
35 .3 3.7
30 .5 7.1
25 1.4 23.9
20 1.8 31.3
15 1.9 33.1
10 2.0 35.0
5 2.1 37.8
0 2.1 37.8
5 left 2.05 35.8
10 1.9 33.1
15 1.8 31.3
20 1.6 27.6
25 1.3 22.1
30 1.1 18.4
35 1.0 16.5
38 .7 . 11.0
40 .15 .9
90 .1 5.4 0

red reflector.A, same type

Angle of incidence, zero degrees. Galvanameter deflection .7
divisions. Galvanometer deflection for 100% reflection 5.4 divisions.
Amount reflected in percent is 13%. It should be noted that the .1
division deflection for ninety degree incidence is due to scattered
light, and that this amount must be subtracted from the other deflec-
tions in order that the actual deflection may be found. This data

is plotted on graph 11.

‘C

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Page 30

Table IV

Green reflector B (cats eye type)

‘Angle of Galv. deflec- % of
incidence in Galv. tion for 100% light
degrees deflection reflection reflected
90 right .1 5.45 0
40 .15 .7
55 .7 11.1
50 .9 14.8
25 .9 14.8
20 .9 14.8
15 .9 14.8
10 .9 14.8
5 .8 15.0
0 .8 15.0
5 left .8 15.0
10 .8 13.0
15 .85 15.9
20 .9 14.8
25 .85 15.9
50 .8 15.0
55 .7 11.1
40 .25 2.7
41 .2 1.8
90 .1 5.2 0
5.4
mean 5.55

,Above data plotted on graph II

Table V

Correction factors

Calculated‘% subtract from

calculated %
50 .55
45 .52
40 .28
55 .24
5O .21
25 .18
20 .14
15 .10
10 .07

5 .04

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Page 31

Table VI

Green reflector C (cats eye type)

Angle of Galv. deflec- i of
incidence in Galv. tion for 100% light
degrees deflection reflection reflected
90 right .1 5e4
57 .5 5.6
56 .5 9.0
55 .7 11.0
50 .9 14.7
25 1.1 18.4
20 1.5 22.2
15 1.4 25.0
10 1.6 27.5
5 1.8 51.5
0 1.8 51.5
5 left 1.7 29.4
10 1.6 27.6
15 1.5 25.7
20 1.5 22.2
25 1.1 18.4
50 1.0 18.4
55 .85 15.8
40 .4 5.5
41 .2 1.8
42 .1 O
90 .1 5.4 0

This data is plotted on graphs II and III

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Page 32

Table VII

Green reflector 0 (cats eye type) rotated 9dafrom data in Table VI

. to check on reflector symmetry.

Angle of Galv. deflec- % of
incidence in Galv. tion for 100% light
degrees deflection reflection reflected
90 right .1 5.5 0
39 .2 1.8
35 1.0 16.1
30 1.1 17.9
25 1.3 21.4
20 1.5 25.0
15 1.7 28.6
10 1.8 30.4
5 1.85 31.3
0 1.85 31.3
5 left 1.8 30.4
10 1.7 28.6
15 1.5 25.0
20 1.3 21.4
25 1.1 17.9
30 .9 14.6
35 .7 10.7
40 .4 5.4
41 .2 1.8
42 .1
90 .1 5.8
5.4

mean 5.56

This data is plotted on graph III.

 

 

 

Page 35

The efficiency of central triple retroreflectors for different angles

of incidence. Auto bulb operating at 8 volts, 3.86 amperes.

Table VIII
lhite reflector
Galv. Deflec- % of
Angle of Galv. tion for 100% light
incidence in deflection reflector reflected
degrees
90 right .1 18.3 0
5O .1 O
45 .2 .5
40 .2 .5
55 .3 1.1
50 .6 2.7
25 1.05 5.2
20 4.2 22.3
15 6.9 32.1
10 7.45 39.9
5 7.8 41.9
0 7.8 18.2 41.9
5 left 7.4 39.7
10 6.5 34.8
15 5.8 31.0
20 4.8 25.5
25 3.9 20.6
30 2.9 15.2
35 2.0 10.3
40 1.5 7e6
45 .9 4.3
50 1.0 prim 4e9
55 2.0 refraction 10.3
60 .9 4.3
65 e4 106
70 .1 0
90 .1 18.3 0
mean 18.26
or 18.3

This data is plotted on Graphs IV and V

Reflector was oriented with reference spot on rear in position indicated
for installation. Figure nine represents one facet in this reflector.
The reflector was rotated about a vertical axis. The word right in

the first column means that right side of figure nine was rotated into

Page 36

the paper about the axis, and the word left means that the left side
of the figure was rotated into the paper.
The reflector was now rotated in the holder ninety degrees, and the

data following was taken for different angles of incidence.

Table II
lhite reflector
Angle of Galv. deflec- % of
incidence in Galv. tion for 100% light
degrees deflection reflection. reflected
90 right .1 18.2 0
50 .1 0
45 e2 05
40 e2 e5
35 .5 _ 2.2
30 e9 4e3
25 3.0 15.8
20 5.5 29e9.
15 6.9 36.9
10 7.5 40.2
5 7.9 . 42.3
0 7.9 18.2 42.3
5 left 7.4 39.7
10 6.8 36.4
15 5.9 31.5
20 4.4 23.4
25 2.3 12.0
30 .8 3.8
35 .3 1.1
40 .2 .5
45 .15 .3
50 .1 0
90 .1 18.4
18.3
mean 18.5

This data is plotted on graph V.

Page 37

Table ‘1

Green central triple retroreflector

Angle of Galv. Galv. deflec— % of
incidence deflection tion for 100% light
in degrees reflection reflected
90 right .1 17.7 0
65 .l 0
60 .2- .6
55 .2 .6
5O .3 1.1
45 .4 1.7
40 .6 2.8
35 - .8 4.0
30 1.0 5.1
25 1.2 6.2
20 1.5 7.9
15 2.1 11.4
10 2.4 13.1
5 2.5 13.6
0 2.5 13.6
5 left 2.3 12.5
10 2.0 10.8
15 1.8 . 9.6
20 1.2 6.2
25 ' .9 4.5
30 .7 3.4
35 .5 2.3
40 .4 1.7
45 e2 .6
50 .2 e5
55 .1 0
90 .1 17.4 0
17.5

mean 17.5
This data is plotted on Graphs IV and VI.
This reflector has a line through the center of the reflector, dividing
the reflector into two equal halves. Figure nine shows a facet. The
cube face on the left side of this figure in the reflector is nearest
the center line. This same face of the facets on the other side of

the center line also is nearest the center line.

 

1‘

 

Page 38

The green reflector in table I was rotated in its holder ninety degrees.

Table XI
Angle of Galv. Galv. deflect- % of
incidence deflection ion for 100% light
in degrees reflection reflected
90 right .1 18.0 0
4O .1 0
55 .2 .5
50 .7 5.5
25 1.4 7.2
20 1.9 10.0
15 2.1 11.1
10 2.4 12.7
5 2.5 15.2
0 2.5 17.8 15.2
5 left 2.5 15.2
10 2.2 11.6
15 1.9 10.0
20 1.7 8.8
25 1.1 5.5
50 .6 2.7
55 .2 .5
40 .1 0
90 .1 18.1 0

mean 18.0
This data is plotted on graph VI
Yellow central triple retroreflector is 'identical in design with
retroreflector measured above.
Angle of incidence was zero degrees
Galvanometer deflection was 3.9 divisions
Galvanometer deflection for 100% reflection was 15.4, 15.7, 15.3,
mean 15.5

Actual % of light reflected is 25.2%

 

 

 

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Page 42

The cats eye retroreflectors plotted on graph II return a large
proportion of the incident light between twenty-five degrees incidence
on one side to twenty-five degrees incidence on the other. The
reflected light then becomes zero at forty degrees. This is just the
performance which has been desired of them.

Graph III shows that the retroreflector C is quite uniform.in
optical properties. This should be so, as the theory of the reflector
indicates it.

The white central triple reflector plotted on graph IV is of
interest. It returns light at greater angles on one side than it
does on the other. Therefore the reflector should be mounted with
such orientation as to make this greater angle available to the
motorist. The rapid drop of reflected intensity on each side of
normal incidence indicates that the reflector leaks light out the
side after one or two reflections. It would be very desirable to
correct this. Cats eye reflector B is very good in that it has a
flat topped curve, but it is not efficient. The green truck reflector
returns much less of the incident light than does the white. This is
perhaps desirable to some extent. A driver does not want a bright

reflection off the rear of the truck ahead of hbm.

Graph V shows that although the car may be in a very hilly
region, the retroreflectors at the roadside still return a large

amount of light to his eyes.

Page 43

Photographs of Reflector Patterns at Different Angles of Incidence.

At first it was planned to use a densitometer to determine the
intensity of the reflected light as recorded upon a photographic
film placed where the photoelectric cell is placed on the apparatus
diagrammed in figure fourteen. However after the photographs were
examined, the extreme irregularity of the patterns made such a pro-
cedure inadvisable. Therefore the photographs were taken directly
on the paper and as shown in this paper are negatives. Eastman
kodabrom.F 2 smooth single weight paper was used for all photographs.

The next five pages display the patterns Obtained at the
indicated angles of incidence. In the photographs of the central
triple reflector white, it is interesting to note how the reflected
pattern cuts off with a definite shadow. .Also note the rotation of
the cut off pattern when the reflector has been rotated ninety degrees.
The black disk in all photographs indicates approximately the intensity
and diameter of one hundred percent reflection. The workmanship on
the die which made the reflectors is clearly indicated, as well as
the altering of the angles between the cube faces to produce a one
degree cone of light. The large faint disk shown on some photographs
is due to the circular aperature of the paper holder which could not
have glass between the paper and the incident light beams.

The reflected patterns of the cats eye reflectors are instructive.
These pictures show clearly that at angles of incidence other than
axial, a very distorted cone is reflected. This may well cause

the reflected cone to miss the eye altogether.

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Page 49

The last photograph of the reflected pattern of reflector B
indicates how small and distorted the cone is even at axial incidence.
The darkening of the paper generally on one~half of the paper record-
ing the reflected beam is due to scattered light. The apparatus,
inside and out, is rendered as light absorbing as possible. A large
percentage of the scattered light is caused by the diffusing of light

by the aluminum.films on the plates H1 and Ba , Figure 14.

Page 50

Design of Improved Apparatus

To improve the portability several changes suggest themselves.
A cell is needed which has a greater current output which will
permit the use of a zero to fifty microampere meter. If the mirrors
could be made to be about fifty percent transmitting the photocell
would have more light incident upon it.

The limitations of the photovoltaic cell limits the accuracy
of the data. The photovoltaic cell is quite sensitive to infra red
light, which would make the output current change with changing
room temperature. The surface of the cell does not have uniform
sensitivity as the following data shows. The 15/16 inch diameter
spot was incident upon the four quarters of the cell surface
successively. The regions covered overlapped somewhat.

Quarter.A Galvanomster deflection 5.7 divisions

Quarter B Galvanometer deflection 5.2 divisions

QUarter C Galvanometer deflection 5.3 divisions

Quarter D Galvanomster deflection. 5.9 divisions

This shows a difference of about ten percent in deflections which
should be the same. Although extreme care was taken to have the
light in the reflector efficiency experiment incident upon the same
spot each time, errors undoubtedly were made.

Probably if a vacuum emission type photoelectric cell were to
be used in place of the photovoltaic cell, improved laboratory results
could be obtained.

The new photocells being made at the present time have a visual

correction. filter which will make the response curve of the photo-

3y

Page 51

cell very similar to that of the eye. This improved type cell
with correction filter would give results that would compare with the
The data obtained would represent the reflection efficiency

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