Diseases of the eye : a handbook of ophthalmic practice for students and practitioners

Front matter

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Gis hee CE MGSEY, BR A Nh PMS Ad PAP har ere eC ese. [act

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Preface To). The Fighth Edition

In the Eighth Edition of this text-book its chapters have been revised thoroughly in an endeavor to include due reference to the important ophthalmic observations and therapeutic measures which have been made and recommended during the last three years.

A new feature in this edition is the introduction of the metric equivalents of the doses of the remedies and the strengths of the solutions previously recorded only according to the old system. Reference to the following subjects appears for the first time: Clifford Walker’s Method of Testing the Visual Field; Squirrel Plague Conjunctivitis; Swimming Bath Conjunctivitis; Anaphylactic Keratitis; Family Cerebral Degeneration with Macular Changes; the Ocular Symptoms of Disease of the Pituitary Body; Sclerectomy with a Punch (Holth’s Operation); Preliminary Capsulotomy (Homer Smith’s Operation) ; Iridotasis (Borthen’s Method); Thread Drainage of the Anterior Chamber (Zorab’s Operation); Extraction of Cataract in the Capsule after Subluxation of the Lens with Capsule Forceps (Stanculeanu’s Method, Arnold Knapp’s Method); Capsulomuscular Advancement with Partial Resection (Ziegler’s Method); Tenotomy of the Inferior Oblique; Window Resection of the Nasal Duct (West’s Operation).

A portion of the chapter on Iritis has been rewritten, especially as it relates to Autotoxemie Iritis and Iritis Secondary to Mucous Membrane Infections. Lieut.-Col. Elliot has very. kindly written the description of Corneoscleral Trephining, ordinarily known as Elliot’s Operation. To Dr. William M. Sweet the author is indebted for a description of his revised method of localizing foreign bodies within the eye by means of the a-rays. As in previous editions, the section devoted to Skiascopy, or the Shadow Test, is from the pen ef Dr. Edward Jackson. A number of new illustrations have been inserted. The entire work has been reset and appears in a new and greatly improved form.

The author trusts that these additions and alterations will prove to be satisfactory, and he desires again to express his high appreciation of the cordial reception which has thus far been accorded to his work.

G.-E. DES.

1705 Watnut STREET, PHILADELPHIA, Pa.

May, 1916.

GONTENAS

CHAPTER I iN ATE O PTT CATs SEO RIN GLPEING a2) Gah ae eae eM eerie SRM Vea acne mace

Transmission of Light, 17—Refraction, 17—Index of Refraction, 17— Prisms, 18—Refraction through a Prism, 18—Angle of Deviation, 19— Numbering Prisms, 19—Dennett’s Method, 19—Prentice’s Method, 20— Rays of Light, 20—Lenses, 23—Foci of Convex Lenses, 23—Foci of Concave Lenses, 24—Formation of Images by Lenses, 25—Focal Distance of a Lens, 28—Numeration of Lenses, 28—The Diopter, 28—Spheric Lenses, 30— Cylindric Lenses, 30—Toric Lenses, 30—Combination of Lenses, 30— Visual Angle, 34—Visual Acuteness, 35—Limit of Perception, 35—Normal Acuteness of Vision, 35—Accommodation, 35—Angle Gamma, 41—Angle Alpha, 41—Convergence, 43—Meter Angle, 44.

Chapter II Examination Of The Patient And External Examination Of The Ehye

PGENCTVONAT: “LE HSTING) Sy o)2:5 feo secs cui ee TN, Mare came | Direct Inspection of the Eye, 47—Blood-vessels of the Conjunctiva, 49— Temperature of Conjunctiva, 50—Inspection of the Cornea, 50—Diameter of Cornea, 51—Sensibility of Cornea, 51—Oblique Illumination, 51—The Corneal Loupe, 52—The Color of the Iris, 52—The Pupil, 53—Measurement of the Pupil, 54—Mobility of the Iris, 55—Pupil-reflexes, 55—Innervation of the Iris and Explanation of the Pupil-reflexes, 57—Dilatation of the Pupil, 61—Contraction of the Pupil, 62—Convergence Anomalies of the Pupils, 68—Unequal Pupils, 64—Special and Paradoxic Pupil-phenomena, 64—Testing Acuteness of Vision, 65—Light-sense, 66—Color-sense, 67— Method of Holmgren, 67—Method of Thomson, 68—Lantern-test, 69— Pseudo-isochromatic Plates of Stilling, 70—Special Tests, 70—Accommodation, 70—Mobility of the Eyes, 71—Balance of the External Eye Muscles, 71—Orthophoria, 71—Heterophoria, 71—Heterotropia, 71—Esophoria, 72—Exophoria, 72—Hyperphoria, 72—Cyclophoria, 72—The Screen (Cover) and Parallax Tests, 72—Prism Tests, 73— Equilibrium Test, 73— Obtuse-angled Prism Test, 75—Insufficiency of the Oblique Muscles (Cyclophoria), 76—Cobalt Test, 76—The Rod Test, 77—Power of Convergence, 78—Field of Vision, 79—Binocular Field of Vision, 82—Abnormalities of Visual Field and Scotomas, 85—Tension, 86—Proptosis, Exophthalmos, 88 —Position of the Eyes, 88.

Chapter III

REFLECTION. THE OPHTHALMOSCOPE AND ITS THEORY. OPHTHALMOSCOPY

ENS TL) 8 YG 09 i Geen eh aeRO aire eC Sapte EU Na ea ga ay a 10 uk AM tone Reflection, 89—The Ophthalmoscope, 91—Direct Method, 92—Size of the Image, 95—Indirect Method, 95—Size of the Image, 96—Ophthalmoscopy, 96—Direct Method of Ophthalmoscopy, 96—Examination of the Cornea

CONTENTS and Lens by Transmitted Light, 98—Examination of the Vitreous, 99— Location of Opacities in the Transparent Media, 99—The Optic Nerve, 100—The Blood-vessels, 101—Physiologic Variations, 102—The Retina, 104—Macula Lutea, 104—The Choroid, 105—Determination of Refraction by the Ophthalmoscope, 106—Ophthalmoscopy by the Indirect Method, 108—Ophthalmodiaphanoscopy, 110—Ophthalmometry, 110— Optometry, 111—Skiascopy, 111—The Use of Mydriatics, 117.

Chapter IV

Emmetropia, 120—Ametropia, 121—Hyperopia, 121—Determination and Correction of Hyperopia, 123—Ordering of Glasses, 125—Myopia, 127— Determination and Correction of Myopia, 133—Treatment of Myopia, 135 —Ordering of Glasses, 136—Astigmatism, 188—Seat of Astigmatism, 138— Regular Astigmatism, 141—Recognition of Astigmatism, 143—Correction of Astigmatism, 143—Ordering of Glasses, 146—Irregular Astigmatism, 147—Surgical Treatment of Astigmatism, 147—Anisometropia, 148— Presbyopia, 148—Correction of Presbyopia, 149—Bifocal Lenses, 153— Spectacles and their Adjustment, 154.

Chapter V

Congenital Anomalies, 158—Edema of the Lids, 160—Erythema of Lids, 160—Urticaria, 160—Erysipelas, 161—Abscess of the Lid, 161—Furuncle of the Lid, 161—Blastomycosis of the Eyelid, 161—Hordeolum, 162— Exanthematous Eruptions, 162—Eczema of the Lids, 163—Herpes Zoster. Ophthalmicus, 163—Herpes Facialis of the Lids, 164—Blepharitis, 165— Phthiriasis, 168—Sporotrichosis of the Lids, 168—Syphilis of the Lids, 168— Tumors and Hypertrophies, 169—Xanthelasma, 171—Chalazion, 171— Sarcoma, 173—Lymphomas, 174—Carcinoma, 174—Lupus Vulgaris, 176— Lepra, 177—Xeroderma Pigmentosum, 177—Elephantiasis Arabum, 177— Tarsitis, 177—Blepharospasm, 178—Ptosis, 179—Blepharochalasis, 179— Lagophthalmos, 180—Symblepharon, 180—Ankyloblepharon, 180—Blepharophimosis, 181—Trichiasis and Distichiasis, 181—Alopecia of the Eyelids, 181—Entropion, 182—Ectropion, 182—Seborrhea, 183—Milium, 183— Molluscum Contagiosum, 184—Ephidrosis, 184—Chromidrosis, 184— Sebaceous Cysts, 185—Injuries, 185.

Chapter VI

Dismasns.:oF -THH; CONTUNCTIVA .: 3. bh eee eee eee See Wee eaeeen ye si 5

Congenital Anomalies, 187—Hyperemia, 187—Conjunctivitis (Ophthalmia), 188—Simple or Catarrhal Conjunctivitis, 188—Acute Contagious Conjunctivitis, 190—Pneumococcus Conjunctivitis, 191—Influenza Bacillus Conjunctivitis, 191—Swimming-bath Conjunctivitis, 192—Diplobacillus Conjunctivitis, 192—Catarrhal Epidemic Conjunctivitis, 194— Exanthematous Conjunctivitis, 195—Purulent Conjunctivitis, 195— Conjunctivitis Neonatorum, 195—Inclusion-blenorrhea of Newborn, 203— Purulent Conjunctivitis in Young Girls, 203—Gonorrheal Conjunctivitis,

‘204—Metastatie Gonorrheal Conjunctivitis, 207—Non-specific Purulent

Conjunctivitis, 207—Croupous Conjunctivitis, 208—Diphtheritie Con-

PAGE

CONTENTS 11 PAGE junctivitis, 209—Phlyctenular Conjunctivitis, 211—Vernal Conjunctivitis, 212—Follicular Conjunctivitis, 214—Granular Conjunctivitis (Trachoma), 215—Sequels of Granular Lids, 221—Parinaud’s Conjunctivitis, 226— Sporotrichosis of Conjunctiva, 227—Chronie Conjunctivitis, 227—KEgyptian and Military Conjunctivitis, 228—Lacrimal Conjunctivitis, 228— Lithiasis Conjunctive, 228—Toxie Conjunctivitis, 228—Atropin Conjunctivitis, 228—Conjunctivitis Nodosa, 229—Xerophthalmos, 230— Amyloid Disease of the Conjunctiva, 230—Conjunctivitis Petrificans, 230— Pterygium, 231—Pinguecula, 231—Abscess of the Conjunctiva, 231— Eechymosis of the Conjunctiva, 232—Chemosis, 232—Emphysema, 232— Lymphangiectasis, 232—Syphilis, 232—Tumors and Cysts, 233—Lepra, 236—Lupus, 236—Tubercle, 237—Pemphigus, 238—Injuries, 238—Affections of the Caruncle, 239—Argyria Conjunctive, 240.

Keratitis, 241—Phlyctenular Keratitis, 241—Ulcers of the Cornea, 244— Results of Corneal Ulceration, 258—Staphyloma, 259—Keratomalacia, 262—Neuroparalytic Keratitis, 262—Keratitis EK Lagophthalmo, 263— Herpetic Keratitis, 264—Rosacea Keratitis, 265—Keratitis Bullosa, 265— Vascular Keratitis, 265—Parenchymatous Keratitis, 266—Keratitis Punctata Syphilitica, 272—Keratitis Punctata, 272—Keratitis Profunda, 273—Keratitis Superficialis Punctata, 273—Keratitis Marginalis Profunda, 274—Keratitis Disciformis, 275—Grill-like Keratitis, 275—Marginal Degeneration of the Cornea, 276—Epithelial Dystrophy of the Cornea, 276— Filamentous Keratitis, 277—Riband-like Keratitis, 277—Blood-staining of the Cornea, 278—Arcus Senilis, 278—Conical Cornea, 278—Hydrophthalmos, 280—Injuries, 280—Traumatic Keratitis, 280—Foreign Bodies, 281—Relapsing Traumatic Keratitis Bullosa, 281—Wounds, 282—Burns and Scalds, 282—Peripheral Annular Infiltration of the Cornea, 283— Traumatic Striped Keratitis, 283—Obstetric Injuries, 284—Tumors and Cysts, 284—Congenital Anomalies, 285.

CHAPTER VIII PHSMASHRNOHe REM AOCLHRA |. 0 Pest g cee Shoe he. ay at eee oes EUR abana: 287 Episcleritis, 287—-Fugacious Periodic Hpiscleritis, 288—Scleritis, 288— Sclerokerato-iritis, 290—Annular Scleritis, 291—Posterior Scleritis, 291— Staphyloma, 291—Abscess and Ulcers, 292—Tumors, 292—Injuries, 292— Foreign Bodies, 293—Congenital Pigmentation, 297—Blue Sclerotics, 298.

Congenital Anomalies, 299—Hyperemia, 301—Iritis, 301—Types of Iritis, 306—Syphilitic Iritis, 306—Rheumatic Iritis, 310—Gouty Iritis, 312— Diabetic Iritis, 312—Gonorrheal Iritis, 313—Scrofulous Iritis, 314—Infectious Disease Iritis, 314—Traumatic Ivitis, 314—Sympathetic Iritis, 314— Secondary Iritis, 315—Serous Iritis, 315—Chronie Iritis, 315—Operations for Iritis, 315—Tumors, 316—Tubercle,-317—Sarcoma, 318—Injuries, 318 —Foreign Bodies, 319—Iridodialysis, 319—Rupture of the Sphincter, 320— Displacement of the Iris, 320—Anomalies of the Anterior Chamber, 320.

Contents

CHAPTER X

DISEASES OF THE CruIARY Bopy AND SYMPATHETIC IRRITATION AND INFLAM-

RATNON 28 ie ey ot Wants Gk, ara enn scat oe arate Sen Sanat Creal eR Cyclitis and Iridocychtis, 322—Plastic Cyclitis, 322—Purulent Cyclitis, 323— Uveitis or Serous Cyclitis, 323—Injuries of the Ciliary Body, 329— Syphilis of the Ciliary Body, 329—Tumors of the Ciliary Body, 331— Sympathetic Irritation, 331—Sympathetic Infammation (Ophthalmitis), 331.

Chapter I

Transmission of Light.—By light is meant that physical force or form of energy which, acting on the sentient elements of the retina, causes the mental perception of the specific energy, that is, sight or vision.

From each point of the surface of a luminous body light or rays of light proceed in straight lines in all directions, and in order to explain the transmission of light it is assumed that throughout the universe there exists an exceedingly tenuous matter to which the term ether is applied (see page 20). Exactly what the vibrating disturbances are which constitute light is not certainly known.

Refraction.—By refraction of light is meant the alteration which takes place in the direction of luminous rays, which pass obliquely from one medium into another of different density.

A ray of light passing through air keeps the same direction until it strikes obliquely the surface of a denser medium, when its course is changed toward the perpendicular to that surface. If this denser medium is a piece of glass bounded by parallel sides, the ray, as it passes through the second surface, is bent back again into the rarer medium.

_ Rays passing from a denser into a rarer medium are deviated from

the perpendicular. The ray now has a direction parallel to its original course; the sides being parallel, the deviation at each surface is equal in extent, but opposite in direction (Fig. 1).

If the denser medium is bounded by oblique surfaces, the deviation at the second surface does not restore the ray to its original direction, but it still more increases the alteration of its direction (Fig. 2).

Index of Refraction.—The deviation of the ray from its course depends upon the difference in the density of the two media.

A ray passing obliquely from one medium into another of the same density is not bent from its course. The relative resistance of a substance to the passage of light is expressed by its indewx of refraction. The absolute index of refraction is its resistance as compared with vacuum; but as there is very little difference between the indices of refraction of air and of vacuum, air is considered as 1 for all calculations - in lenses.

2 ; 17

As the difference in the density of the two media increases, the ray is bent more sharply from its course, and the angle it forms with the perpendicular after refraction by a denser medium is proportionably smaller than the angle formed by the ray before refraction.

Fig. 1.—Refraction of light through a plate of glass bounded by plane surfaces which are parallel: A—B is the incident ray; B—C, the same ray, refracted by the first surface, nearer to the perpendicular, P—P; C—D, the same ray, refracted by the second surface, becomes parallel to A—B, its original direction. The ray H—K, perpendicular to the surfaces B and C, undergoes no refraction.

The angle formed by the ray with the perpendicular to the surface of the second medium is called the angle of incidence—angle I. The angle formed by the ray with the perpendicular after refraction is called the angle of refraction—angle R. The sine of the angle of incidence, divided by the sine of the angle of refraction, gives the index of refraction. Glass used in the manufacture of spectacles has an index of refraction of about 1.53.

Prisms.—A prism is a portion of glass or other refracting substance bounded by two plane surfaces which

Fig. 2.—Refraction through a are inclined to each other, forming an denser medium having oblique surfaces. : é =i At each surface the ray is bent toward angle, which is called the refracting the base of the figure. angle, or simply the angle of the prism

(Fig. 2, a), and is expressed in degrees. Prisms are often designated by the numbers of degrees in the refracting angle.

The sides of the prism converge to a thin edge at one extremity, called the apex (Fig. 2, A); at the other extremity they diverge from each other and form the base (Fig. 2, B-C).

Refraction Through a Prism.—If a ray of light from an object (Fig. 2, O) passes through a prism the refractive index of which is greater than air, the deviation is always from the apex toward the base of the prism.

To the eye of an observer placed at the other side of the prism (Fig. 2, FE) the refracted ray seems to come from the direction of the

NUMBERING OF PRISMS 19 apex (Fig. 2, 0’), since a ray is projected backward over the course given to it by its last refraction, and a single object appears double if, with both eyes open, a prism of sufficient strength is placed before one of them. The angle which the ray in this last direction forms with the ray in its original direction is called the angle of deviation.

When one eye, on account of muscular weakness, is unable to direct its visual line to the point of fixation, a prism will alter the direction of the ray from the point of fixation so that it coincides with the visual line of the weaker eye. The refractive properties of a prism are utilized to test the strength of the ocular muscles (see pages 74 and 555), to neutralize the diplopia caused by. abnormal deviation of the visual line—for example, in paralytic strabismus and in the treatment of heterophoria (see page :559)—to detect malingerers who feign monocular blindness (see page 505), and in the application of the Wildbrand-Saenger test to determine the situation of the lesion in hemianopsia (see page 518). Fig. 3.—Deviation pro-

Angie of Deviation.—The angle of de- , dues] by > prim. I, Bnele of

caesar x Rt ia incidence; R, angle of refracviation is the angle formed by the incident tion; D, ‘angle of deviation; ray with the refracted ray. The amount ee Bea Rey of this angle is somewhat more than one-half of the refracting angle of the prism for all prisms between 1° and 10°, but for practical purposes the two may be considered equal. Above this the deviation rapidly increases.

When the angle of incidence, formed by a ray in the interior of a prism, amounts to 40° 49’, the angle of refraction equals 90°; the angle of deviation, the difference between the two, then equals 49° 11’.. When the refraction which takes place at each surface of a prism is equal, the minimum amount of deviation is present. When the ray is perpendicular to one surface, the angle of incidence at the second surface equals the angle of the prism; the deviation is greater in this case, as all the refraction takes place at one surface. A table of the minimum deviation of prisms is given on page 20.

Numbering of Prisms.—The designation of prisms by their angular deviation, instead of by their refracting angles, was urged by Dr. Edward Jackson, of Denver, before the Ninth International Medical Congress. ‘Two methods of accomplishing this have been proposed:

Dennett’s Method: The Centrad.—Dr. William S. Dennett’s calculation has for its base an arc called the radian, whose length equals the radius of its curvature. Such an arc equals 57.295°. A prism which will produce an angular deviation of the one-hundredth part of this are is called one centrad. The deviation of such a prism would, therefore, be 0.57295°. The merit of this method consists in the uniformity of the deviation, 10 centrads having exactly ten times the deviation of 1 centrad. The deviations are so many hundredths of the radius measured on the are.

Prentice’s Method: The Prism-diopter.—Mr. Charles F. Prentice proposes, as the standard of deviation, a prism which shall deflect a ray of light 1 cm. at a plane 1 meter distant—that is, the hundredth part of the radius measured on the tangent. This he calls the prism-diopter. 'The value of the centrad and prism-diopter are given below (see table).

There are two practical advantages connected with the method of Mr. Prentice which also can be applied to the centrad. The prismatic deviation of a decentered lens may be very readily found, as Prentice has shown by the following rule: If a lens be decentered 1 cm., the prismatic deviation of the lens will be equal to as many prism-diopters as the number of diopters in the lens. Thus, if a 4-diopter lens be decentered 1 cm., the prismatic deviation will be 4 prism-diopters, or 4 centrads, since centrad and prism-diopter exactly equal each other. The same lens decentered 0.5 cm. would produce 2 prism-diopters or centrads of deviation.

Table of Relative Values of Centrads and Prism-diopters, Prepared by

James Wallace.

Refracting angle of

Centrads. Prism-diopters. prism required. 1 Mase EE Aa eRe mA ey ay Fear Eo.) ice) (ata sOielbsat Met hen enn Me Racer ah 1.06° DAO a tee ie send a ZOOS ese er CENT are Die 2.16% BS ea eee irate Paneer HoT 34 00) WS RIL ent aN rar eM Sage 3:24° Aine ea at ne rte rk See Ne BE OQO ZS tive nee Ao 4,32° LS AIA PEEPS kel NOMSR AEOE Wy a TePe DOOD Are Rae ae Neen ee 5.40° Ce eee a aM enthey Cas trains GLOOGS ey pee ape 6.47° HUse ones T aCe Pane Chace EDC is UI Hoye etehso ay atime ayaa 7.54° Co Nts FV ra Ne BR et ee toy 0) NSPE NODE Delete pare i aly 8.62° Uae ea eters Nas ae DOD A Ae eee i laasnena ee rere n ie 9.68° 1 O55 Se ale ie eonoa aor Ma urna OOS SORA otk Catered ieee HOH IES ees ea EM AB in ea aay 2 Ua: ER AES acc rR ST 6.1° PARE Ric AMON IS ETT oat o DOD LO iaiss werner ek ccs Peake aaa Zilelon 40 “Biche ese Net kaa Rs eae Re RRO Name Foe eee 39.0073°

The prisms represent the minimum deviation wh an index of refraction of 1.53.

The relation to the meter angle (see page 44) is also very simple. One-half the interpupillary distance is the sine of the meter angle. The ratio of this to the point of fixation in hundredths gives nearly the number of prism-diopters, or centrads of deviation, embraced in any number of meter angles. For example, if the interpupillary distance is 60 mm., one-half of this is 30 mm.;-assuming the amount of convergence to be 4 meter angles, 25 cm., or 250 mm., is the distance of the point of fixation. The deviation of the visual line then is 30 in 250, or 12 in 100 = 12 centrads, or 12 P. D. For small arcs the tangent and the sine agree very closely with the arc. Four meter angles of convergence then represent 12 centrads of deviation or 12 prism-diopters.

Rays of Light.—Any luminous point diffuses light in all directions in straight lines called rays. As the rays proceed from the luminous source, those which diverge from one another become more widely separated (Fig. 4).

RAYS OF LIGHT 21

If a circular aperture 1 cm. in diameter be made in a metal plate and a luminous point be placed at different distances from it—for example, at 1 meter and at 10 meters—the rays coming from 10 meters, which pass through the aperture, will be less diverging than those which come from 1 meter. A cone of light will pass through the aperture in each case, but the shape of it will be different according to the distance of the light from the aperture in the screen. When the round hole, 1 cm. in diameter, is 1 meter distant from the point of light, the cone has a base 1 cm. in diameter, and the apex is situated in the luminous point 100 cm. distant.

The rays have diverged 1 cm. in traveling 100; the metal plate has cut off all other rays having a greater divergence.

If the cone of light passes through the aperture and falls upon a distant wall, the cone will preserve the same proportions— viz., the base will be zo of the altitude.

‘If the wall be 5 times the distance of the screen from the light, a luminous circle 5 Fig. 4-—Divergence of rays from

i 5 és a luminous source (Loring).

em. in diameter will be formed upon the wall. If, now, the light is removed to a point 10 meters from the screen (1000 cm.), a cone of light is formed whose base is 1 cm. and whose altitude is 1000. The rays which pass through the aperture have now only 35 of the divergence of the rays in the former case; the base of the cone is toca of the altitude. The cone of light will now form a circle on the wall 5 meters beyond the aperture, only 1.5 em. in diameter. If the point of light be at a very great distance, there will be no

Fig. 5.—Rays diverging from the candle A pass through the aperture in the screen S, and form the cone of light whose base is the distance a—a’. Rays from a more distant candle, B, having a greater divergence than b—-b’, are intercepted by the screen S (Wallace).

difference in the size of the luminous circle and the aperture in the screen; the size of the circle remains about 1 em. on the wall at 5 meters from the screen. The rays, therefore, have a nearly parallel direction. This is shown in Fig. 5.

Rays which enter the pupil of the eye from a point 6 meters distant have so little divergence that they may be considered parallel. The average size of the pupil being 4 mm., the divergence is only sov- All rays diverging more widely than this are excluded by this width of the pupil.

The relation to the eye of rays diverging from 6 meters or coming from an infinite distance is practically identical, but for lenses of long focal distance and large aperture an infinite distance is required in order to obtain parallel rays. Thus the sun and stars are so remote that the rays coming from them have no appreciable divergence, and they are considered parallel.

Parallel rays must emanate, as has been explained before, from a distant object. They are brought together by a lens at its principal focus. Conversely, rays which diverge from the principal focus of a lens are parallel to one another after being refracted by the lens

Divergent rays emanate from an object nearer than infinity. A greater refractive power must be exercised to bring them together at the same distance behind a lens than is required for rays which are parallel; consequently, divergent rays are united at a point farther than the principal focus. The nearer the point of divergence lies to the lens, the farther away from the lens is the point where the rays converge to a focus.

Fig. 6.—Lenses as prisms.

Convergent rays do not exist in nature. Only such rays are convergent which have passed through a convex lens or have been reflected from a concave mirror.

Significance of the Different Rays.—The refraction of the eye is determined by the character which the rays must have in order to be brought to a focus on the retina.

An emmetropre eye, with relaxed accommodation, requires rays to be parallel in order that they shall meet on the retina.

A myopic eye requires rays to diverge from some near point in order to meet on its retina.

A hyperopic eye requires rays which already have convergence to some point in order to unite them on its retina.

An emmetropic eye emits parallel rays.

A myopic eye emits convergent rays.

A hyperopic eye emits divergent rays.

CONJUGATE FOCUS OF A CONVEX LENS 23

Lenses.—A lens is a portion of glass or other transparent substance bounded by two curved surfaces, or by one curved surface and one plane surface. The curved surfaces are convex, elevated in the center, and thin at the edge; or they are concave, hollowed out in the center and thick at the edge.

A lens may be regarded as a series of prisms with the refracting angles increasing in value from the center toward the periphery.

In a convex lens the bases of the prisms are directed toward the center of the lens, and rays, therefore, are refracted toward the axis which passes through the center. In a concave lens the bases of the prisms are directed away from the center, and rays, therefore, are refracted away from the axis. As the angles increase from the center outward, the peripheral rays will be refracted more than the central rays. The result of this is that in a convex lens the rays after refraction converge to the same point, the increased bending of the more peripheral rays just sufficing to compensate for their greater distance from the axis. In a concave lens the rays diverge more widely as they

Fig. 7.—Principal focus of a convex lens. The parallel rays a, b, c, d are refracted by the lens so as to unite at the point F on the axis P. The ray P undergoes no refraction. F is the principal focus.

pass through the peripheral parts of the lens, with the result of making them appear to have diverged from a common point.

Focus of a Convex Lens.—The point to which rays converge after refraction by a convex lens is called its focus.

Principal Focus of a Convex Lens.—The principal focus of a lens is the focus for parallel rays. As the most distant rays are only parallel, never convergent, the principal focus is the shortest focus, unless the lens is combined with another convex lens or concave mirror. Rays diverging from the principal focus of a lens are rendered parallel after passing through the lens, and come to a focus at an infinite distance.

Conjugate Focus of a Convex Lens.—When rays diverge from any point nearer than infinity, they are brought together at a point on the other side of the lens farther than the principal focus. The point from which rays diverge and the point to which they converge are called conjugate foci. As the point of divergence approaches the lens the point of convergence recedes; when the point of divergence is at twice the focal distance of the lens, the point of convergence is at an equal distance on the other side. The conjugate foci are now equal.

As the point of divergence approaches still closer the point of convergence is at a greater distance, until, when the point from which the rays diverge is at the principal focus, the rays converge at an infinite distance.

Fig. 8.—Conjugate focus of a convex lens. The two dots in the axis represent the principal foci, one being marked F. Rays diverging from O converge after refraction to the point F’, farther than the principal focus. Rays from F’ also converge after refraction to O. O and F are conjugate foci.

Rays diverging from either of these points converge toward the other. When rays diverge from a point whose distance is equal to or greater than the principal focus, the conjugate focus is positive. When the distance is less than the principal focus, the conjugate focus is negative.

Virtual Focus of a Convex Lens.—When rays diverge from some point nearer to a lens than its principal focus, the rays after refraction still continue divergent. These divergent rays, if traced backward,

Fig. 9.—Virtual focus of a convex lens. Rays from the point O, less than the principal focal distance, diverge after refraction as if they came from the point V. V is the virtual focus of O.

would meet in a point on the same side of the lens from which they diverged. This point is called a negative, or virtual, focus, because the rays do not really meet here, but are given a direction by the lens as if they had diverged from this point (Fig. 9). Therefore the point from which rays diverge and the point to which they converge are focal oints.

: Foci of Concave Lenses.—The foci of concave lenses for parallel or divergent rays are virtual, or negative. They are the points from which the rays seem to diverge after passing through the lens.

FORMATION OF IMAGES BY A LENS: OPTICAL CENTER 25

Principal Focus of a Concave Lens.—When parallel rays fall upon a concave lens they are rendered divergent. If these rays be traced backward, they will seem to have diverged from a point near the lens. This point is the principal focus (Fig. 10).

Fig. 10.—Principal focus of a concave lens. Parallel rays a, 6b, d, e, after refraction by the concave lens L, are rendered divergent as if they came from the ‘point F on the axis c. Theray cis not refracted. F, the principal focus of a concave lens, is virtual.

Conjugate foci of concave lenses are also virtual and found in a similar manner.

Formation of Images by a Lens: Optical Center.—In the lens (Fig. 11) the point O on the axis is called the optical center. Any ray

Fig. 11.0, Optical center of lens. The point C” is the center of curvature for the surface S’’. The point C’ is the center of curvature for the surface S’. A ray passing from C” to C’ would be perpendicular to both surfaces. It would pass through without deviation. This ray is called the axial ray, or azis.

The radii C’—J” and C’—J’, being parallel, a ray in the lens passing in the direction J’—J” must form equal angles at the two surfaces. The point where this ray intersects the axis is the optical center (Landolt).

passing through this point is refracted equally at both surfaces, since it forms equal angles with the radii of the two surfaces. The direction of the ray is, therefore, the same after refraction by the second surface as it was before refraction by the first. For thin lenses it may be said that any ray directed to the optical center passes through without deviation. ‘These rays are called secondary axes.