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Visual Perception

Notice

Medicine is an ever-changing science. As new research and clinical experience broaden our knowledge, changes in treatment and drug therapy are required. The author and the publisher of this work have checked with sources believed to be reliable in their efforts to provide information that is complete and generally in accord with the standards accepted at the time of publication. However, in view of the possibility of human error or changes in medical sciences, neither the author nor the publisher nor any other party who has been involved in the preparation or publication of this work warrants that the information contained herein is in every respect accurate or complete, and they disclaim all responsibility for any errors or omissions or for the results obtained from use of the information contained in this work. Readers are encouraged to confirm the information contained herein with other sources. For example, and in particular, readers are advised to check the product information sheet included in the package of each drug they plan to administer to be certain that the information contained in this work is accurate and that changes have not been made in the recommended dose or in the contraindications for administration. This recommendation is of particular importance in connection with new or infrequently used drugs.

Visual Perception

A C L I N I C A L O R I E N T A T I O N

FOURTH EDITION

Steven H. Schwartz, OD, PhD

State College of Optometry

State University of New York

New York, New York

New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto

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ISBN: 978-0-07-160462-8

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Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

1. Experimental Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 1

2. Introductory Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 3

Very Basic Ocular Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .3

Basic Retinal Anatomy and Postretinal Pathways . . . . . . . . . . . . . . . . . . .

. .6

Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.20

Transmission Characteristics of the Eye . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3. The Duplex Retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Basic Distinctions Between Scotopic and Photopic Vision . . . . . . . . . . . . .

26

Morphological Distinctions Between Rods and Cones . . . . . . . . . . . . . . . .

26

Photopigments in Rods and Cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

Retinal Distribution of Photoreceptors . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

Dark Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Light Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Spatial Resolution and Spatial Summation . . . . . . . . . . . . . . . . . . . . . . . . .

47

Temporal Resolution and Temporal Summation . . . . . . . . . . . . . . . . . . . . .

51

Stiles–Crawford Effect of the First Kind . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

4. Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

Photometry and Radiometry: Basic Concepts and Units . . . . . . . . . . . . . . .

65

Cosine Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Inverse Square Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

v

vi

Contents

 

 

Retinal Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .74

 

Scotopic Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.75

 

Derivation of the Photopic Luminosity Function . . . . . . . . . . . . . . . . . . .

.77

 

Specification of Light Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.79

 

Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.82

 

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.91

 

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.92

5.

Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.93

 

Trichromatic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.93

 

Absorption Spectra of the Cone Photopigments . . . . . . . . . . . . . . . . . . . .

102

 

Grassman’s Laws of Metamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

104

 

Color Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107

 

Wavelength Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

 

Bezold–Brücke Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111

 

Color Constancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112

 

Physiological Basis of Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

 

Munsell Color Appearance System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

119

 

CIE Color Specification System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

120

 

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

128

 

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

6. Anomalies of Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

 

Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

 

Basic Data of Inherited Color Vision Anomalies . . . . . . . . . . . . . . . . . . . .

133

 

Color Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141

 

Inheritance of Anomalous Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . .

144

 

Molecular Genetics of Red–Green Color Vision Anomalies . . . . . . . . . . .

145

 

Acquired Color Vision Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

148

 

Achromatopsias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

150

 

Chromatopsias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

150

 

Standard Color Vision Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151

 

Nagel Anomaloscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

 

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

 

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167

 

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

168

7.

Spatial Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

169

 

Sine Wave Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

169

 

Fourier Analysis: Basic Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

173

 

Spatial Modulation Transfer Function of a Lens . . . . . . . . . . . . . . . . . . . .

174

 

The Human Contrast Sensitivity Function . . . . . . . . . . . . . . . . . . . . . . . .

177

 

CSF High-Frequency Cutoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

177

 

CSF Low-Frequency Drop-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

182

 

The Visual System as a Fourier Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . .

183

 

Relationship of CSF to Snellen Acuity . . . . . . . . . . . . . . . . . . . . . . . . . . .

187

Contents

vii

Clinical Implications of the CSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.190

Clinical Determination of the CSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

193

Other Forms of Visual Acuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

195

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

199

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

200

8. Temporal Aspects of Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201

Stimulus Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201

Temporal Modulation Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . .

204

More on the CFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

208

Other Temporal Visual Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

209

Masking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

214

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

215

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

217

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

218

9. Motion Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219

Stimuli Used to Study Motion Perception . . . . . . . . . . . . . . . . . . . . . . . . .

219

Dorsal Processing Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

223

Roles of Luminance and Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

223

Dynamic Visual Acuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

224

Saccadic Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

225

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

226

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

227

Self-Assessment Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

228

10. Depth Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

229

Monocular Depth Cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

229

Binocular Depth Cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

236

Size Illusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

237

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

239

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

241

Self-Assessment Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

242

11. Psychophysical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

243

Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

243

Determination of Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

245

Signal Detection Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

252

Weber’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

260

Magnitude of Sensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

265

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

267

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

268

12. Functional Retinal Physiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .269 The Retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .270 Receptive Fields of Ganglion Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271 Recording from Retinal Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .276

viii Contents

Photoreceptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .276

Horizontal Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .279

Bipolar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .279

Amacrine Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284

Ganglion Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .290

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .290

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .291

13. Parallel Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 293

What the Frog’s Eye Tells Its Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.294

X- and Y-Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

295

Parvo and Magno Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

296

Functions of the Parvo and Magno Pathways . . . . . . . . . . . . . . . . . . . . . .

300

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

302

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

306

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

307

14. Striate Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

309

Basic Organization of the Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

309

Simple and Complex Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

311

Edges or Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

318

Striate Cortical Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

318

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

324

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

324

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

325

15. Information Streams and Extrastriate Processing . . . . . . . . . . . . . . . . . . .

327

Information Diverges Beyond Striate Cortex . . . . . . . . . . . . . . . . . . . . . .

327

Cortical Modularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

328

Role of Area MT/V5 in Motion Perception . . . . . . . . . . . . . . . . . . . . . . .

330

IT and Form Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

332

Role of V4 in Binocular Rivalry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

333

A Word About Visual Attention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

333

Visual Agnosias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

338

Phantom Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

340

Are There Grandmother Cells? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

341

Can Vision Be Trained? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

341

A Word of Caution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

342

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

343

Self-Assessment Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

344

16. Gross Electrical Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .345

Electrooculogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .345

Electroretinogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .348

Visually Evoked Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .357

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .362

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .363

Contents

ix

17. Development and Maturation of Vision . . . . . . . . . . . . . . . . . . . . . . . . .

. 365

Deprivation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.365

Amblyopia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

370

Meridional Amblyopia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

376

Perceptual Consequences of Bilateral Visual Deprivation . . . . . . . . . . . . .

379

Development of Refractive Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

380

Development of Grating Acuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

382

Development of Other Visual Attributes . . . . . . . . . . . . . . . . . . . . . . . . . .

387

Additional Clinical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

391

Vision in the Later Years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

392

Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

400

Answers to Self-Assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

401

Chapter 3: The Duplex Retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

401

Chapter 4: Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

402

Chapter 5: Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

404

Chapter 6: Anomalies of Color Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . .

405

Chapter 7: Spatial Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

406

Chapter 8: Temporal Aspects of Vision . . . . . . . . . . . . . . . . . . . . . . . . . . .

409

Chapter 9: Motion Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

409

Chapter 10: Depth Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

409

Chapter 11: Psychophysical Methodology . . . . . . . . . . . . . . . . . . . . . . . . .

410

Chapter 12: Functional Retinal Physiology . . . . . . . . . . . . . . . . . . . . . . . .

410

Chapter 13: Parallel Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

410

Chapter 14: Striate Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

411

Chapter 15: Information Streams and Extrastriate Processing . . . . . . . . .

411

Chapter 16: Gross Electrical Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . .

412

Chapter 17: Development and Maturation of Vision . . . . . . . . . . . . . . . .

412

Practice Examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .415

Practice Examination 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .415

Practice Examination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .425

Practice Examination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .435

Answers to Practice Examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447

Answers to Practice Examination 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447 Answers to Practice Examination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .448 Answers to Practice Examination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .449

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

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