Refraction and how to refract : including sections on optics, retinoscopy, the fitting of spectacles and eyeglasses, etc

Front matter

Chap. Copyright No..—.

Shelf]

UNITED STATES OF AMERICA.

Preface

This book has been written at the request of the many students who have attended the author's lectures on "Refraction" at the Philadelphia Polyclinic; and while it is intended for all beginners in the study of Ophthalmology, yet it is especially for those practitioners and students who may have a limited knowledge of mathematics and who can not readily appreciate the classic treatise of Donders.

In the preparation of the manuscript and in arranging these pages the writer has planned to be systematic and practical, so that the student, starting with the consideration of rays of light, is gradually brought to a full understanding of optics ; and following this, he is taught what is the standard eye, and then is given a description of ametropic eyes, with a differential diagnosis of each, until finally he is told how to place lenses in front of ametropic eyes to make them equal to the standard condition.

By being dogmatic rather than ambiguous, with occasional repetitions to avoid frequent references, and by simple explanations and a definite statement of facts, the writer has aimed to make the text more concise and comprehensive than if encumbered with lengthy mathematic formulas or with any discussion of disputed points.

The chapter on Retinoscopy embraces descriptions of that method of refracting, both with the plane and with the concave mirror ; but no matter how carefully expressed, the

VI PREFACE.

student will frequently confuse the two, and he is therefore referred to the author's manual on " Retinoscopy with the Plane Mirror."

Of the two hundred illustrations used to elucidate this work, nearly all are newly made, and were drawn or photographed by the author. Those in colors, on page 145, and the diagrams of astigmatic eyes, as also several others, are original.

The author desires to tender his thanks to Dr. Helen Murphy, of Philadelphia, and to Dr. J. Ellis Jennings, of St. Louis, Mo., for many valuable suggestions.

120 S. 1 8th St., Philadelphia, Pa.

November, i8gg.

Preface To Second Edition

The first edition of this work was published in November, 1899, and it is indeed gratifying to the author that the work has found such favor as to call for a second in so short a time.

In preparing this edition and to make it more lucid than the first, the writer has carefully reviewed the original text and made some changes in the phraseology.

The writer takes this opportunity to thank his many friends and correspondents, at home and abroad, for their complimentary letters and reviews, which are gratefully appreciated.

September, igoo.

Chapter II

The Eye. — The Standard Eye. — The Cardinal Points. — Visual Angle. — Minimum Visual Angle. — Standard Acuteness of Vision. — Size of Retinal Image. — Accommodation. — Mechanism of Accommodation. — Far and Near Points. — Determination of Distant Vision and Near Point. — Amplitude of Accommodation. — Convergence. — Angle Gamma. — Angle Alpha, 58

Chapter XII

Lenses, Spectacles, and Eye-glass Frames. — How to Take Measurements for Them and How They Should be Fitted, 285

INDEX, 295

LIST OF ILLUSTRATIONS.

~IG. PAGE

1. Reflection, 12

2. Reflection from Plane Mirror, 12

3. Lateral Inversion, 13

4. Reflection from Concave Mirror, 14

5. Erect Image Formed by Concave Mirror, 15

6. Inverted Image Formed by Concave Mirror, 16

7. Image Formed by Convex Mirror, 17

8. Perpendicular to Plane Surfaces, 18

10. Critical Angle, 19

11 and 12. Angle of Refraction, 20

13. Density, 20

14. Index of Refraction, 21

15. Maximum Deviation, 22

16. Minimum Deviation, 22

17. Angle of Deviation, 23

18. Displacement, 24

19. Centrad, 24

20. Prism Diopter, "24

21. Neutralization of Prisms, 25

22. Correction of Diplopia, 28

23. 24, and 25. Convex Lenses, 29

26, 27, and 28. Concave Lenses, 30

29. Peripheral Refraction Through a Convex Lens, 30

30. Peripheral Refraction Through a Concave Lens, 30

31. Parallel Rays Passing Through a CorfVex Lens, 31

32. Parallel Rays Passing Through a Concave Lens, 32

33. Conjugate Foci, 33

34. Ordinary Foci, 34

35. Negative Focus, 35

36. Secondary Axes, . .» 35

37. Optic Center, 36

38. Inverted Image Formed by a Convex Lens, . . 37

39. Erect Magnified Image Formed by a Convex Lens, 39

40. Image Formed by a Concave Lens, 39

41 and 42. Cylindric Lenses, 43

43. Cylinder Axis, 43

44. Parallel Rays Passing Through a Convex Cylinder, 43

45- Parallel Rays Passing Through a Concave Cylinder, 44

46. Trial -case, . . 45

ix

LIST OF ILLUSTRATIONS.

FIG. PAGE

47 and 48. Trial- frames, 46 and 47

49. Combining Sphere and Cylinder, 49

50, 51, and 52. Finding Optic Center of a Lens, 54

53 and 54. Finding Cylinder-axis, 55

54, 55, and 56. Action of a Cylinder, 55 and 56

57. Standard Eye, 59

58. Angle of View, 60

59 and 60. Size of Retinal Image, 61

61. Minimum Visual Angle, 62

62 and 63. Five-minute Angle, . 63

64. Retinal Image in the Standard and Ametropic Eyes, 64

65. Crystalline Lens at Rest and Accommodating, 67

66. Accommodation, 68

67. Hyperopic Eye at Rest, 70

68. Myopic Eye at Rest, 71

69. Randall' s Test-letters, 73

70. Wallace Test-letters, 74

71. Illiterate Card, 74

72. Gould's Test-letters, 75

73. Gothic Type for Testing Near Point, 79

74. Block Letters for Testing the Near Point, 80

75. Meter Angle of Convergence, 82

76. Angle Gamma, 83

77. Positive Angle Gamma, 84

78. Negative Angle Gamma, 85

79. Loring Ophthalmoscope, 87

80. Direct Ophthalmoscopy, ... I 88

81. Emmetropia with the Ophthalmoscope, .... 94

82. Hyperopia with the Ophthalmoscope, 95

83. Myopia with the Ophthalmoscope, 96

84. Indirect Ophthalmoscopy, 98

85. Condensing Lens, 98

87. Emmetropic and Ametropic Eyes 23 mm. Long, 102

88. Hyperopic Eye at Rest, 105

89. Hyperopic Eye Refracted, 105

90. Parallel Rays Entering a Myopic Eye . . . no

91. Myopic Eye at Rest, in

92. Myopic Eye Refracted, in

93. Astigmatic Lens, 121

94. Simple Hyperopic Astigmatism, 124

95. Simple Myopic Astigmatism, 125

96. Compound Hyperopic Astigmatism, 125

97. Compound Myopic Astigmatism, 126

98 and 99. Mixed Astigmatism, 127

100. Symmetric Astigmatism, 128

101. Asymmetric Astigmatism, 128

102. Astigmatism with the Rule, 129

103. Astigmatism Against the Rule, 129

104. Placido's Disc, 133

105. Stenopeic Slit, 133

106. Green's Astigmatic Chart, 135

LIST OF ILLUSTRATIONS. XI

FIG. PAGE

107. Astigmatic Clock-dial, 136

108. Astigmatic Clock-dial in Black, 137

109. Author's Pointed Line Test, 139

no. Perforated Disc, 140

in. Pray' s Letters, . 140

112. Scheiner's Disc, 141

113. Scheiner's Disc in Hyperopia, 141

114. Scheiner's Disc in Myopia, 142

115 and 116. Cobalt-blue Glass, 143

117. Refrangibility of Cobalt-blue Glass, 144

118 to 129, inclusive. The Diagnosis of the Different Forms of Ametropia with Cobalt-blue Glass, 145

130. Thomson's Ametrometer, 147

131 and 132. Ophthalmometer, 148 and 149

133 and 134. Mires or Targets, 150

135. Indirect Ophthalmoscopy, 153

136. Author's Schematic Eye, 154

137. Point of Reversal, . 155

138 and 139. Author's Mirror with Folding Handle, 156

140. Author's Iris Diaphragm Chimney, 157

141. Position of Light and Minor, 158

142. High Myopia as Seen with the Concave Minor, 159

143. Hyperopia as Seen with die Concave Mirror, 159

144 and 145. Rate of Movement of Retinal Illumination in Hyperopia

and Myopia, 162 and 163

146. Retinal Illumination in Emmetropia, 164

147. Band of Light, 167

148. Axonometer, . 168

149. Scissor Movement, 170

150. Positive Aberration, 171

151. Negative Aberration, 171

152. Homonymous Diplopia, 173

153. Heteronymous Diplopia, 174

154 and 155. Maddox Rods, 182

156. Rotary Prism of Risley, 183

157. Phorometer, 184

158. Strabismometer, 194

159. Angle of Deviation in Strabismus, 195

160. Monocular Blinder, 197

162 and 163. Franklin Bifocals, 273

164. Morck's Bifocals, 273

165 to 171, inclusive. Cement Bifocals, 274 and 275

172 and 173. Acromatic Bifocals, 275

174 and 175. Solid Bifocals, 276

176 to 180, inclusive. Half Lenses, 277

181. Toric Lenses, 278

182 to 191. inclusive. Different Sizes and Shaped Lenses, . 283 and 286

192. Measuring Interpupillary Distance, 289

193 and 194. Fitting of Spectacle Bridge, 290

195. Measurement of Bridge, 291

196. Measurement for Spectacles, 292

Xll LIST OF ILLUSTRATIONS.

FIG. PAGE

197. Measurement for Eye-glasses, 292

198. Distance Frames, 293

199. Near Frames, 293

200. Measurement for Guards, 293

HOW TO REFRACT.

Chapter I. Optics

Optics (from the Greek o-ro/iac, meaning " to see ") is that branch of physical science which treats of the nature and properties of light.

Catoptrics (from the Greek xdronzpov, meaning " a mirror") and dioptrics (from the Greek d(<>--pov, meaning " to see through ") are subdivisions of optics ; the former treating of incident and reflected rays, and the latter of the refraction of light passing through different media, such as air, water, glass, etc., but especially through lenses.

Light. — Light may be defined as that form of energy which, acting upon the organs of sight, renders visible the objects from which it proceeds. This form of energy is propagated in waves in all directions from a luminous body, and with a velocity in a vacuum of about 186,000 miles a second. In the study of a luminous body, such as a candle-, lamp-, or gas-flame, the substance itself must not be considered as a single source of radiation, but as a collection of minute points, from every one of which waves proceed in all directions and cross one another as they diverge from their respective points. The intensity of light decreases

IO REFRACTION AND HOW TO REFRACT.

as the square of the distance from the light increases : for example, if an object is twice as far from a luminous body as another of the same size, it will receive one-fourth as much light as the latter.

Ray. — Ray (from " radius ") is used in optics in preference to wave, and means the smallest subdivision of light traveling in a straight line. Rays of light are considered as incident, emergent, reflected, refracted, divergent, parallel, and convergent.

Incident Rays. — Rays of light are said to be incident when they strike the surface of an object.

Emergent Rays. — Rays of light are emergent when they have passed through a transparent substance.

Reflected Rays. — Rays of light are reflected when they rebound from a polished surface.

Refracted Rays. — A ray of light undergoes refraction when it is deviated from its course in passing through any transparent substance.

Divergent Rays. — Rays of light proceed divergently from any luminous substance, but, in the study of refraction, only those which proceed from a point closer than six meters are spoken of as divergent.

Parallel Rays. — The greater the distance of any luminous point, the more nearly do its rays approach to parallelism ; this is evident in a study of rays coming from such distant sources as the sun, moon, and stars. For all practical purposes in the study of refraction, rays of light which proceed from a distance of six meters or more are spoken of as parallel, although this is not an absolute fact, as rays of light at this distance still maintain a slight amount of divergence. If the pupil of the emmetropic eye is represented by a circular opening four millimeters in diameter, then rays of light from a luminous point at six meters (6000

OPTICS. I I

mm.) will have a divergence of ^qq when they enter such a pupil.

Convergent Rays. — Convergent rays are the result of reflection from a concave mirror or refraction through a convex lens.

A Beam. — This is a collection or series of parallel rays.

A Pencil. — A pencil of light is a collection of convergent or divergent rays. Convergent rays are those which tend to a common point, whereas divergent rays are those which proceed from a point and continually separate as they proceed. This point is called the radiant point.

A Focus. — This is the point of a convergent or divergent pencil ; the center of a circle ; the point to which converging rays are directed.

A Positive or Real Focus. — This is the point to which rays are directed after passing through a convex lens or after reflection from a concave mirror.

A Negative or Virtual Focus. — This is the point from which rays appear to diverge after passing through a concave lens, or after reflection from a convex mirror, or after refraction through a convex lens when the light or object is closer to the lens than its principal focus, or after reflection from a concave mirror when the light or object is closer to the mirror than its principal focus.

The principal phenomena of light are absorption, reflection, and refraction.

Absorption. — Rays of light from the sun falling upon the green grass are partly absorbed and partly reflected. The grass absorbs some of the rays and sends back or reflects only those rays which together produce the effect of green. A piece of red glass owes its color to the fact that it transmits only that portion of the light's rays whose combined effect upon the retina is that of red. The relative

REFRACTION AND HOW TO REFRACT.

proportion of absorption and reflection of rays of light greatly depends upon the quality of the surface — whether light colored or polished, or dark colored or rough.

Reflection. — From the Latin reflectere, " to rebound." This is the sending back of rays of light by the surface on which they fall into the medium through which they came. While most of the rays falling upon the surface of a transparent substance pass through it, with or without change in their direction, yet some of the rays are reflected, and it is by these reflected rays that surfaces are made visible.

Fig. 2.

A substance that could transmit or absorb all the rays of light coming to it (if such a substance existed) would be invisible. Reflection, therefore, always accompanies refraction, and, if one of these disappear, the other will disappear also.

Laws of Reflection. — (i) The angle of reflection is equal to the angle of incidence. (2) The reflected and incident rays are in the same plane with the perpendicular to the surface. (See Fig. 1.)

If A B represent a polished surface and I the incident ray, then P D I is the angle of incidence ; R being the re-

OPTICS.

fleeted ray, then P D R, equal to it, is the angle of reflection. I D, P D, and R D lie in the same plane.

A reflecting surface is usually a polished surface (a mirror), and may be plane, concave, or convex.

Reflection from a Plane Mirror. — Rays of light are reflected from a plane mirror in the same direction in which they fall upon it : if parallel, convergent, or divergent before reflection, then they are parallel, convergent, or divergent after reflection. An object placed in front of a plane mirror appears just as far back in the mirror as the object is in front of it. (See Fig. 2.)

A B represents a plane mirror with E F, rays from the extremes of the object I, reflected from the mirror A B, and meeting at the observer's eye as if they came from the object I in the mirror. (See Visual Angle, p. 60.) The apparent distance of the object I from the observer is equal to the combined length of the incident and reflected rays.

The appearance of an image in a plane mirror is not exactly the same as that of the object facing the mirror ; it undergoes what is known as lateral inversion. This is best understood by holding a printed page in front of a plane mirror, when the words or letters will read from right to left. (See Fig. 3.) An observer facing a plane mirror and raising his right hand, his image apparently raises the left hand.

Tilting a plane mirror gives an object the appearance of

R r^

E F

1 3

LEC

TION l/IOIT

Fig. 3. — Lateral Inversion.

REFRACTION AND HOW TO REFRACT.

moving in the opposite direction to that in which the mirror is tilted.

Spheric Mirrors. — A spheric mirror is a portion of a reflecting spheric surface ; its center of curvature is therefore the center of the sphere of which it is a part. Spheric mirrors are of two kinds — concave and convex.

Reflection from a Concave Mirror (Fig. 4). — Parallel rays are reflected from a concave mirror, and are brought to a focus in front of it. This point is called the principal focus (P.F.). The principal axis of a concave mirror is a straight line drawn from the mirror through the principal focus and

Fig. 4.

the center of curvature (i-i), and a secondary axis (2' , 2', 2', 2 r ) is any other straight line passing from the mirror to the center of curvature (C.C.). Rays which diverge from any point beyond the principal focus are reflected convergently (G J). Rays which diverge from any point closer than the principal focus are reflected divergently (V V).

Images Formed by a Concave Mirror. — To find the position of an image as formed by a concave mirror, two rays may be used : one drawn from a given point on the object to the mirror, and parallel to its principal axis, and reflected through the principal focus (P.F., Figs. 5 and 6) ; the other, the secondary axis, from the same point, passing

OPTICS.

through the center of curvature. The place where the secondary axis and the reflected ray or their projections intersect gives the position of the image. Unlike the plane mirror, which produces images at all times and at all distances, the concave mirror produces either an erect, virtual, and enlarged image, as an object is placed closer than its principal focus, or an enlarged inverted image if the object is between the principal focus and the center of curvature.

By withdrawing the mirror in the former instance the erect image increases slightly in size, and in the latter the inverted image diminishes in size. At the principal focus there is no image formed.

Fig. 5.

Figure 5 shows an erect, virtual, and enlarged image of A R which is closer to the mirror than the principal focus. Parallel rays from A and R are reflected to the principal focus, P.F. Lines drawn from the center of curvature through A and R to the mirror are secondary axes ; these lines and those reflected to the principal focus do not intersect in front of the mirror, but if projected, will meet at a and r behind the mirror, forming a magnified image of A R. If the mirror is withdrawn from the object, the erect magnified image will increase in size, but at the principal focus no image will be formed, as the rays are reflected parallel.

ID REFRACTION AND HOW TO REFRACT.

Figure 6 shows a real inverted image of A R at a r ; A R situated beyond the principal focus. Lines drawn from A and R through C.C. are secondary axes. Parallel rays from A and R converge and cross at the principal focus (P.F.).

Where D P and F E intersect the secondary axes, the inverted image a r of A R is situated. When the object, as in this instance, is situated beyond the center of curvature, the image is smaller than the object. As the image and object are conjugate to each other, they are interchangeable, and in such a case the image would be larger than the object and inverted. This is always true when the

Fig. 6.

object is situated between the center of curvature and the principal focus. When an object is situated at the center of curvature, its image is equally distant and of the same size, but inverted.

Tilting a concave mirror gives an object placed inside of its principal focus the appearance of moving as the mirror is tilted ; but if the object is situated beyond the principal focus, the object appears to move in the opposite direction.

Reflection from a Convex Mirror. — All rays are reflected divergently from a convex mirror, and parallel rays diverge as if they came from the principal focus situated behind the mirror at a distance equal to one-half its radius

OPTICS.

of curvature. The principal focus of a convex mirror is therefore negative. The foci of convex mirrors are virtual.

Images Formed by a Convex Mirror. — These are always virtual, erect, and smaller than the object. The closer the object, the larger the image ; and the more distant the object, the smaller the image. Tilting a convex mirror, the image does not appear to change position.

In figure 7 parallel rays from the object A R are reflected from the mirror as if they came from the principal focus situated at one-half the distance of the center of curvature, C.C. Lines drawn from the extremes of the object to C.C. are

A r^

-_-_.

.

P.F.

...

J

F

*

Fig. 7.

secondary axes, and the image is situated at the point of intersection of the secondary axes and the rays from the principal focus ; and as these meet behind the mirror, the image is virtual and erect.

Refraction. — From the Latin r ef ranger e, meaning " to bend back " — i. e., to deviate from a straight course. Refraction may be defined as the deviation w r hich takes place in the direction of rays of light as they pass from one medium into another of different density.*

* As ordinarily understood in ophthalmology, refraction has come to mean the optic condition of an eye in a state of repose or under the physiologic effect of a cycloplegic.

i8

REFRACTION AND HOW TO REFRACT.

Two laws govern the refraction of rays of light :

1. A ray of light passing from a rare into a denser medium is deviated or refracted toward the perpendicular.

2. A ray of light passing from a dense into a rarer medium is deviated or refracted away from the perpendicular.

Aside from these laws, there are other facts in regard to rays of light that should have consideration. A ray of light will continue its straight course through any number of different transparent media, no matter what their densities, so long as it forms right angles with the surface

ICE

FLINT GLASS

CROWN

PLATE

Fig. 8.

or surfaces. Such a ray is spoken of as the normal or perpendicular ; such surfaces are plane, the surfaces and perpendicular forming right angles. (See Fig. 8.) In any case of refraction the incident and refracted rays may be supposed to change places.

Figure 9 shows the perpendicular (P P) to a piece of plate glass with plane surfaces. The ray in air incident at O on the surface S F is bent in the glass toward the perpendicular, P P. The dotted line shows the direction the ray would have taken had it not been refracted. As the ray in the glass comes to the second surface at R, and passes into a rarer medium, it is deviated from the perpendicular, P P. The ray now continues its original direction, but has been deviated from its course ; it has undergone lateral displacement.

Critical Angle or Limiting Angle of Refraction. — This is the angle of incidence which just permits a ray of light in a dense medium to pass out into a rare medium. The size of the critical angle depends upon the index of refraction of different substances. Figure 10 shows an electric light suspended in water. The ray from this light which forms an angle of 48 ° 35' with the surface of the water

Fig. 10. — Critical Angle.

will be refracted and pass out of the water, grazing its surface ; but those rays which form an angle greater than 48 35' will not pass out of the water, but will be reflected back into it. The surface separating the two media becomes a reflecting surface and acts as a plane mirror.

The critical angle for crown glass is 40 ° 49/.

Index of Refraction. — By this is meant the relative density of a substance or the comparative length of time required for light to travel a definite distance in different substances. The absolute index of refraction is the density or refractive power of any substance as compared

REFRACTION AND HOW TO REFRACT.

with a vacuum. According to the first law of refraction, a ray of light passing from a rare into a dense medium is refracted toward the perpendicular ; in other words, the angle of refraction is smaller, under these circumstances, than the angle of incidence. In the study of the comparative density of any substance it will be seen that the angle of refraction is usually smaller the more dense the substance ; this is well illustrated in figures 1 1 and 12.

The greater the density, the slower the velocity or the more effort apparently for the wave or ray to pass through the substance. This is illustrated in figure 13, where a ray or wave of light is seen passing at right angles through different media. A ray passes through a vacuum without apparent resistance, but in its course through air it is slightly impeded, so that air has an index of refraction of r

A

/ J

I

Ice

Glass

Diamond

Vacuum

Air

1.00029 -f- when compared with a vacuum ; but as this is so slight, air and a vacuum are considered as one for all purposes in refraction. To find the index of refraction of any substance as compared with a vacuum or air, it is necessary to divide the sine of the angle of incidence by the sine of the anoje of refraction.

OPTICS.

In figure 14 the angle of incidence P C I is the angle formed by the incident ray I with the perpendicular, P P. The angle of refraction P C R is the angle formed by the refracted ray with the perpendicular, P P. Drawing the circle P H P O around the point of incidence C, and then drawing the sines D X and B F, perpendiculars to the perpendicular P P, divide the sine D X of the angle of incidence by the sine F B of the angle of refraction to obtain the index of refraction ; in this instance, water as compared with air. D X equaling 4 and F B equaling 3, then 4 divided by 3 will equal |-, or 1.33 -f, the index of refraction of water as compared with air.

To find the index of refraction of a rare as compared with a dense substance, divide the sine of the angle of refraction by the sine of the angle of incidence — i. e., air as compared with water would be ^, or 0.75.

p

/ Air \

C ]

\ Water p

Indexes of Refraction.

Crown glass, 1. 5

Flint glass, 1.58

Crystalline lens, nucleus, 1.43

" " intermediate layer, 1.41

" " cortical layer, 1.39

REFRACTION AND HOW TO REFRACT.

A prism is any refracting substance bounded by plane surfaces which intersect each other. The sides of a prism are the inclined surfaces. The apex is where the two plane surfaces meet. The base of the prism is the thickest part of the prism. The refracting angle is the angle at which the sides come together.

Position of a Prism. — When a prism is placed in front of an eye, its position is indicated or described by the direction in which its base is situated : base down means that the thick part of the prism is toward the cheek ; base up means that the thick part of the prism is toward the brow ; base in means that the thick part of the prism is toward the nose ; and base out means that the thick part of the prism is toward the temple.

Prismatic Action. — Rays of light passing through a prism are always refracted toward the base of the prism. If an incident ray is perpendicular to the surface of a prism, there will be only one refraction, and that takes place at the point of emergence. The angle of incidence in this instance will equal the angle of the prism, and the maximum deviation takes place, as all the refraction is done at one surface.

In figure 1 5 the incident ray (I) is perpendicular to the surface A B, and is not refracted until it comes to the surface A C at E, when it is bent toward the base B C, all the refraction taking place at the surface A C.

If an incident ray forms an angle other than a right angle with the first surface of the prism, then it will be refracted twice — as it enters and as it leaves the prism.

In figure 16 X N is the perpendicular to the surface A B. The ray (I) incident at N is refracted toward this perpendicular and follows the course N E inside of the prism. On emergence it is refracted from the perpendicular E P of the surface A C, and in the direction of the base of the prism. If the incident ray (I) so falls upon the surface A B that the refracted ray (N E) is parallel to the base (B C), and the emergent ray is such that the angle of emergence equals the angle of incidence (I N X), as in this instance, then the angles of incidence and of emergence are equal, and the deviation is at a minimum, or the least possible.