Thomas G. (Thomas George) Atkinson.

Essentials of refraction online

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Sp Thomas G. Atkinson, M. D.


G. P. ENGELHARD al witli pathological dis-
eases of the eye, it has been thought wise to include a
chapter briefly describing those ocular diseases wliieli
are intimately connected with disturbances of vision,
and for whieli, therefor.', the refractionist is frequently
first consulted. Thus warned, the refractionist can, by
a very reasonable exercise of care, readily detect and
identify these conditions, and promptly refer tluin to
the oculist for appropriate treatment.

Special attention is given to the use of the oi.htlial-
moscope and retinoscope. These instniments have for
many years en'oyed a deserved popularity among En-

ropoati refractionists in tlie estimation and correction
of refractional errors, and the author believes they are
destined to attain equally general favor in this country.

The illustrations are from a series of entirely new
and original drawings, designed with a view of eluci-
dating those points which the author's experience has
demonstrated to be essential points, most happily
demonstrable by means of diagrams, but which, unfor-
tunately, are not as a rule made the subjects of illus-
trations in text books of refraction.

The present edition represents practically an entire
rewriting of the book, and the addition of sections on
optical principles and hygiene of the eye, thus making
a complete manual on all that pertains to the art and
science of refraction.

Chicago, January 2, 1914.


Chapter I Light 9

Chapter II Optics — Visibility ID

Chapter 11 1 Tii e Eye 35

Chapter lY Eefkactiox of the Eye. . . 47

Chapter Y Lenses 57

Chapter YI Accommodation and

Convergence G3

Chapter Yll Retinoscopy 77

Chapter YIII Ophthalmoscopy 97

Chapter IX Correction of Hyperme-


Chapter X Correction of Myopia 121

Chapter XI Correction of Astigma-
tism 127

Chai)ti'r XIT Practical Instructions.. 141
Clia})ter XI 1 1 Strabismus and Imbal-
ance 153

Chapter XTY Asthenopia 1(>9

Chapter XY Diseases of the Eye Con-
nected WITH Disturb-
ance OF YisioN 179

Chapter XYF ErrTixo the Classes 191

Chanter X \' 1 1 11 vcue XE of tue Eye 215



Nature and Source of Light.

Lit/hi is a I'oi'iii (•[' j»liysical i'iu'i\av, which, at-t-
in^- upon the retina ol' the ('>i\ produces in the
brain the sensation of vision.

The same word, Light, is used in physiology to
designate the sensation thus produced. This,
however, is not the optical significance of the

Genekatiox of Light. — The commonest
modes of generation of light are (1) the chemical
process of combustion, and (vM the nioh'cular
activity of friction.

SouKCKS. — The chief source ot light is the sun,
in which probably chemical and molecuhir activ-
ity both take i^ai't. The light generated by the
sun is called Natural light. Other common
sources of light are lamps, candles, gas (cond)us-
tion), and latterly electric light (friction). Light
thus generated is called Artiiicial light.

XATrHK.-^The exact nature of light, like that
of other forms of physical energy, is not as yet
understood. We are able to recognize and study
it onlv tlirough its effects upon the material
uu^vlia which it intiuences, or whidi influence it.
hi a general way it is understood to consist of an
oscillatory vil)ration of the panicles of ether.

TuANSA.nssiox. — The utilization of light re-
quires its transmission from one point to another


in si:»ace through suitaljle media. This is accom-
plished bv the vi1)rations communicating them-
selves to adjoining particles of th(- >ame medium
or to those of another medium.

It sliould be understood, of course, that actually
light vibrations are never communicated from one
medium to another, since light vibrations are per-
tinent only to ether. What actually happens is
that the vibrations are communicated from the?
ether in the interspaces of one medium to the
ether in the interspaces of another medium. But
for working convenience we say that they are
communicated from one medium to another.

Transparency and Opacity. — Media or
bodies which permit of this transmission of light
vibrations through their substances are called
transparent. Those which do not are called

Transparent and opaque are, of course, relative
terms, simply denoting the comparative capacity
of different media for transmitting light vibra-
tions. Probably no form of matter is either ab-
solutely transparent or absolutely opaque.

Every medium of greater density is more or
less opaque as compared witli one of less density.
Tliat is to say, the light vibrations of a rarer
medium, are never completely communicated to
a denser medium, some of them ])eing turned back
by the denser into tlie rarer medium.
. Transmission — Absorption — Eeflectiox. —
Of those vibrations which are communicated to a


modiniii, ^nmo pass throiiiTli it and arc re-com-
imiiiii-att'd to anotlier luediuin; others exhaust
themselves upon the substance of the medium and
are transfoi'ined into other forms of energy. The
f(U"mc'r are said to be tninsniifh'd, the hitter ah-
sorhciJ. \)\ the medium. Tliose which are turned
back by a denser medium into a rarer medium arc
said to be reflected.

Every medium — i. e., every form of matter —
absorbs light vibrations to a more or less extent.

Dynamics of Light.

The dynamics of light inchule a consideration
of the modes of franstnisslon , relocHy. force, and
effects upon matter, of its vibrations.

Method of Transmission. — Light vi])rations
al-e supposed to travel in the form of waves; that
is to say, the path of the transmitted vii)ration is
marked by an alternate expansion and contrac-
tion, or, to speak more correctly, an alternate rari-
fication and condensation, of the medium, ulti-
niiilcly due. of course, to the alternate repulsion
and attraction of its atoms.

Velocity. — Light vibrations are estimated to
travel through space — i. e., through luminous
ether — at a speed of 186,300 miles per second.
This, however, is an average estimate, since even
ether offers some resistance to their ])assage, and
therefore their velocity progressively decreasres
during transmission.

The velocity of light vibrations varies directly



as the force of their propulsion (impetus) and
inv.crsoly as the density of the medium.

Force. — Xo satisfactory basis has been deter-
mined for the computation of the force or impe-
tus of light vibrations. Hence in practical op-
tics eacli source of liglit is taken as an independ-
ent standard, and the second factor, viz., the

Illustrating- the different oscillatory Avave lengths.

c()m})arative densities of the media through which
the vibrations pass, is the only factor regarded
in tlie determination of their relative velocity.
The denser the medium the more slowly the vi-
brations travel.

OsciLLAToia' Velocity. — In addition to the ve-
locity of their transmission, light vibrations have
a lateral or oscillatory velocity, dependent upon
tlic size of tlie vibratoiT wave — i. e., upon the
range of repulsion and attraction communicated
to tlie particles of ether. The larger the wave —
i. e., the greater the range of this repulsion and
attraction — tlu* less the oscillatory velocity.

Effects of Light Upon Matter.

Outride of the already mentioned fact that light
\il)rations propagate themselves through different
forms of matter at varying velocities and under



van'ing ooiulition.^, iiotliiiig is known of any
pnrol}' (Ivnaniic effects produced by them upon
objective media wliivli is of any parlicular \aliie
in a study of optics. 1Mie only effects which con-
cern optics are those which light vibrations pro-
duce upon the retina and are sul)jectively inter-
preted by the eye.

IntfIxsity. — The relative transmission-velocity
of liglit vil)rations produces an effect upon the
retina which the l)i'ain interprets as comparative
intensity of light. There are, as will presently
be seen, other conditions of the ocular apparatus
itself which intluence intensity, but so far as the
vibrations themselves are concerned, the more
ra[)idly thev ai'c traveling when they strike the
retina the more intense the sensation of light pro-
duced, it is for this reason, among others, that

IHustrating- the resultant straight path of tlie lig:ht
vibrations, constituting the ray.

light received from a near point appears more
intense than that I'lom a fai' point. Tliis cor-
responds to the loudness of sound.

Color. — The relative oscillatory velocity — in
other words, the relative wave-length — of light
vibrations is responsible, through its effects upon
the retina, for sensations of color. The more rapid
-these oscillations — i. e.. the shorter the waves — •
the higher the color. The shortest perceptible
light-waves gives the sensation of violet; the long-


est, that of deep red. This corresponds to pitch
in sound.

Geometries of Light.

Closely allied to the dynamics of light, ])ut
technically distinct from them^ are its geometric
relations, upon which the whole system of op-
tics, so far as it relates to refraction, is based.

Linear Propagatiox. — Foremost of these geo-
metric postulates is the well-known axiom that
light yibrations are propagated in a straight line,
and cannot be made to trayel in any other kind
of course. This is what makes it necessary for
an object to be in our uninterrupted line of yision
in order that we may see it.

Rays. — For optical purposes, therefore, the yi-
brations themselyes are not regarded as such. The
imaginary straight lines in which they trayel are
regarded as the units of light, and are called rays.
A combination of rays, representing the passage
of seyeral yibrations of ditferent wayc-lengths^ is
called a penciL

DiyERGEXCE OF Eays. — Kays of light leaying
an object, whether reflected or generated by the
object, are projected in a diyergent manner and
in all ayailable directions, and doubtless continue
to diyerge as long as they remain in the same

Infinite Rays. — At a certain distance from
their origin, the angle of diyergence of those rays
which come within our range of yision is so slight
that it is impossible to show that they are not



parallel, and for optical purposes they are then
regarded as parallel. Experience has shown this
distance to l)e six meters or over. Kays, there-
fore, M'liicli oriuiiiale six meters or more from the

Showing how the angle of reflection CBP is equal
to the angle of incidence ABP.

observer are said to come from infinity, are called
infinite rcn/s^ and are regarded as parallel.

Finite I^ays. — Rays which proceed from an
object less than six meters from the observer are
called finite rays, and are divergent.

Reflection. — As previously stated, when rays
of light strike the surface of a denser nuMlium not
all of them are communicated to the new medium,
some of them being turned back into the rarer
medium. These are said to be reflected. The re-
flecting power of a medium is proportionate to
the smoothness of its surface.

Angle of Incidence and Reflection. — The
angle which a ray striking such a surface makes
witli the pci'pondieular of tlio >urface is called the



angle of incidence. The angle which the same
ray makes with the same perpendicular after re-
flection is called the anole of reflection.

Illustrating' how a ray AB, upon entering a denser
medium, is bent toward the perpendicular, as BC, and
iipon entering a rarer medium is bent away from the
perpendicular, as CD.

Laavs of Ekflection. — Eeflection takes place
in accordance with two geometric laws, viz. :

1. The angle of incidence is equal to the angle
of reflection.

2. The incident and reflected rays are hoth in
the same plane, which is perpendicular to the
reflecting surface.

Eefractiox. — "When a ray of light passes from
one medium into another of different density, if
the surface of the medium into which it passes
is perpendicular to the ])nth of the ray it con-
tinues to travel in the same straight line.

If, however, the surface of the receiving me-
dium is not perpendicular to the ray, the latter,
upon entering it. is hent or deflected from its


course. This bending of a ray is called Refrac-
tion. If it passes into a denser medium it is bent
toward the perpendicular of the surface; if into a



Illustrates the index of refraction. AB represents
the incident ray entering- the surface of the refracting
medium; B C the refracted ray. XY is the sine of
the ang-le XBY made by the incident ray with the per-
pendicular PP'. X'Y' is the sine of the angle X'BY'
made by the refracted ray with the same perpendicu-
lar. The ratio between XY and X'Y' is the index of
refraction of the two media.

rarer medium it is bent away from that perpen-

Index of Refraction. — Naturally, the rela-
tion of the angle of incidence — i. e., the angle
which a ray striking such a surface makes with
the perpendicular — to the angle of refraction —


i. e., the angle which the same ray makes with
the same perpendicular after refraction — is not
uniform, as in the case of reflection, but varies
with the comparative densities of the respective

For optical purposes we estimate the degree of
refraction by comparing the sine of the angle of
incidence with the sine of the angle of refrac-
tion, and the ratio between these two geometric
quantities is called the index of refraction of one
medium as compared with the other.

For working convenience we regard air as the
standard medium, and the ratio between the sines
of the angles which a ray of light makes with the
perpendicular before and after passing from air
into a given medium is said to be the index of
refraction of that medium. The index is plus or
minus according as the ratio is in favor of or at
the expense of the angle of refraction.

Example : A ray of light passing from air
into water and refracted by the water. The sine
of the angle of incidence is 1.333 times greater
than the sine of the angle of refraction. There-
fore the index of refraction of water is said to
be -f 1.333.

N. B. — In optics, so far as they relate to re-
fraction of eyes, we never have to do with any re-
fracting medium of less density than air. Hence
the index of refraction of those media which con-
cern us is always plus, and no attention need be
paid to minus indices.


The visibility of an object is clue to (1) its
capacity for reflecting part, but not all, of the
rays of light which strike its surface, and (2)
its ability to change the dynamic qualities of
those rays which it reflects. An object which
either transmits, or absorbs, or reflects all of the
rays which it receives is not visible as an object.

Showing- how (vision being- wholly due to reflected
rays) an object which transmits all the rays and re-
flects none of them is invisible to the eye.

An object which perfectly transmits all of the
rays which strike its surface is absolutely invis-

An object which completely absorbs all of the
rays which reach it is seen simply as an area of



An object which uniformly reflects all of the
rays which strike its surface is seen sheerly as an
area of light, similar in all respects to the source
of its illumination.


Showing how an object like a mirror, which reflects
all the rays is itself invisible but appears to the eye
in all respects as the original source of light.

Those substances which we usually regard as
being quite transparent (air, crystal glass, water,
etc.) perfectly transmit some of the rays and
uniformly reflect others, so that we both "look
through them'^ and also see them as an area of
pure light.



An object which is visible in detail absorbs
part of the light rays which strike its surface
and reflects others, according to the various form
and character of its surface. Those rays which

Showing- how an object which transmits some rays
and reflects some is visible to the eye as an individual

it reflects are changed in velocity, wave-length,
etc., also in accordance with the varied surface
of the object^ and effects are produced upon the
retina corresponding to these changes. The net
sum of these effects constitutes what is known
as the retinal image, from which the brain judges
of the identity of the object.

The more nicely balanced the absorption and
reflection of light, the more clearly the object is


seen. In ordinary sunlight there is too much
reflection; this is why we see things in much
clearer detail just after sun-down.

Eeflected Image. — All retinal images are
tliereforo reflected images. However, when the
light is reflected directly from the object to the
retina we say that we see the object itself. It is
manifest that an object can be thus seen only when
it is in an uninterrupted straight line with the
retina. When the light from an object is inter-
cepted by another surface, and by it reflected
to the retina we speak of the retinal image being
a reflected image. By this means an object may
become visible which is not in the direct line of

Reflection of Light.

A body with a highly and imiformly polished
surface, which does not transmit light, reflects
practically all of the rays which strike its sur-

When the light reflected by such a surface
comes from a source of pure light, it is seen, as
already stated, as an area of pure light, similar
to the source of illumination.

AVhen, on the other hand, the light so reflected
reaches the polished surface from another object,
it is reflected in all respects in the same condi-
tion as it was received from the original object,
and makes precisely the same effect upon the
retina as thougli roeeived by the eye from tlie



original object. In other words, the mirror gives
a' reflected image of the object.

Projection. — Since light always travels in a
straight line, the brain is only able to project
light rays — that is, to refer them to an origin, in
a straight line. Hence the image of an object
seen in a mirror does not appear to the brain to


Illustrating the apparent position of a reflected

he located at the original object but on a straight
line projected from the retina through the point
at which the rays strike the mirror.

But the brain judges of distance by the dy-
namic qualities of the rays which reach the retina,
and these have-not been changed by the process
of reflection. 'Fherefore the distance at which
the image a{)}X3ars to be located is the distance
which tlio rays have actually traveled— namely.



the distance from the object to the mirror plus
the distance from the mirror to the eye.

The apparent location of the reflected image
from a plane mirror, therefore, is in a straight

Showing how parallel rays are focused by a con-
cave mirror at a point F, midway between the surface
S and the optical centre C. The distance SF is the
focal length of the mirror.

line from the eye through the reflection point on
the mirror, as far beyond the mirror as the ob-
ject is from the reflection point.

Concave Reflection of Light.

A concave surface is to be regarded as made
up of a number of plane surfaces inclined to-
ward each other.

The optical center of a concave mirror is the



center of the sphere of whiclj the concave surface
is a segment.

Principal Focus — Focal Length. — Parallel
rays, falling upon a concave mirror, are reflected

Illustrating conjugate foci, F and' F'. If tlie light
be at F the reflected image will focus at F', but if the
light be at F' the image will focus at F.

as convergent rays which meet at a point on the
axis midway between the surface of the mirror
and the optical center. This point is called the
principal focus of the mirror, and the distance
from the surface to this point is called the focal
length of the mirror.

Con/ersely it follows that rays originating at


the focal point of a concave mirror are reflected
as parallel rays from the surface of the mirror.

It also follows that rays which originate at the
optical center of a concave mirror are reflected
back from the mirror in the same lines, and the
object is its own image.

Com JUGATE Foci. — If the origin of the rays be
at a point within the optical center (but not with-
in the principal focus) the reflected rays will con-
verge at a point an equal angular distance witli-

Illustrating a virtual focus F. The light at L pro-
jected on a concave mirror will appear from any point
between A and B to be at F.

out the center. N"ow if the point of convergence
outside the optical center be made the point of
origin the former point of origin inside the op-
tical center becomes the point of convergence of
the reflected rays. These two points have there-
fore a reciprocal relation to each other, and are
called conjugate foci.

Virtual Focus^ — Virtual Image. — If the rays
originate at a point inside the principal focus of
a concave mirror, by the laws of reflection the



rays are reflected from the surface as divergent
rays, and never meet. As explained above, an
eye in the path of these divergent rays will in-
terpret them as coming from a point in a straight


- ^d-

Illustrating how a real reflected image becomes in-

line from the eye through the point of reflection
on the mirror, and as far behind the mirror as
the originating point is from the surface.

The'point at which tlie image thus appears to
be located is called the virtml focus, and the
image thus seen a virtual image.

A concave mirror therefore gives.two kinds o±
image or no image at all, according to the loca-
tion of the object.

If within the principal focus, it gives an erect
virtual image, because the rays are reflected di-
vergently and never meet.

If at the optical center, there is no image at
all, because the rays are reflected so as to make
the object its own image.



If outside the optical center^ it gives a real
inverted image, because the rays are reflected so
as to meet at a point within the center, and have
therefore crossed before they reach the eye.
Refraction of Light.

Every body or substance which transmits light
exercises more or less power of refraction — i. e.,
it deflects the ray more or less from its original
course, provided the ray strikes its surface at




Illustrating how a virtual reflected image remains

other than a perpendicular angle. By this means,
as well as by reflection, objects may be rendered
visible which are not in an uninterrupted straight
line with the eye.

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Online LibraryThomas G. (Thomas George) AtkinsonEssentials of refraction → online text (page 1 of 12)