A Treatise on Physical Optics

Front Cover
Deighton, Bell, 1892 - Optics - 411 pages
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Contents

Composition of two waves polarized in the same plane
10
Elliptically and circularly polarized light
11
The Principle of Huygens
13
Law of the reflection of light
14
CHAPTER II
17
Fresnels mirrors
19
Production of interference fringes by a biprism
20
do do biplate
21
Fresnels experiment with three mirrors
22
Displacement of fringes by the interposition of a plate
23
Abnormal displacement of the central band Airys explanation
24
Lloyds experiment
25
Examples
26
COLOURS OF THIN AND THICK PLATES
28
Stokes fundamental hypothesis
34
CHAPTER IV
42
Diffraction through a slit
48
Elliptic aperture
56
Resolving power of optical instruments
63
A fine grating produces broad bands Overlapping of spectra
70
Resolution of double stars
77
DIFFRACTION CONTINUED
80
Intensity at the centre of the aperture or disc Poissons theorem
86
On the Bessels function Jn + x where ? is zero or any positive
93
Diffraction by a narrow obstacle
100
Positive and negative uniaxal crystals Principal indices of refrac
108
ABT PAGE 96 Biaxal crystals Equation of FreBnels wavesurface
109
Principal indices of refraction for aragonite and topaz
110
Transparent media when subjected to stress exhibit double refraction
111
CHAPTER VII
112
Discussion of the hypothesis that the vibrations of polarized light are perpendicular to the plane of polarization
113
The optic axes are perpendicular to the circular sections of the ellipsoid of elasticity
116
107108 Values of the two velocities in terms of the angles which the normal to the wavefront makes with the optie axes
117
Determination of the equation of Fresnels wavesurface
118
Traces of the wavesurface on the coordinate planes
119
Singular points Bay axes
120
Geometrical construction determining the direction of vibration in a plane wave
121
Equations of the tangent and normal cones at the singular points
122
Equation of the cone whose vertex is the origin and whose gene rators pass through the circle of contact of the tangent plane at the extremity of an o...
123
Uniaxal crystals Proof of Huygens construction
124
Discovery of conical refraction by Sir VV Hamilton
125
Internal conical refraction
126
Criticisms on Fresnels theory
127
125126 Theory and construction of Nicols prism
128
Polarization by a plate of tourmaline
129
tion of the formation of coloured rings
137
135 Rings produced when the plate is cut parallel to the axis
143
Rings produced by a plate of biaxal crystal whose axes form
149
ArT PAGE 156 Expression for the intensity when a plate of quartz is cut perpen
156
CHAPTER IX
157
THE ELECTROMAGNETIC THEORY
160
Description of the rings and brushes
164
Discussion of the results when the Nicols are crossed
167
do do when the planes of polarization and ana lysation are parallel
169
Expression for the intensity when the incident light is circularly polarized
170
Discussion of the results
172
Two plates superposed one of which is righthanded and the other lefthanded
173
Discussion of the results Airys spirals
174
CHAPTER X
176
Verification of Brewsters law by Sir J Conroy
177
Fresncls theory
178
Values of the intensities
179
Total reflection is accompanied by a change of phase
180
The refracted wave is a superficial wave
181
Reflection and refraction of light polarized perpendicularly to the plane of incidence
182
Proof of Brewsters law
183
Experimental verification of the change of phase which accom panies total reflection FresnePs rhomb
184
Theories of Neumann and MacCullagh
185
Objections to these theories
187
CHAPTER XI
189
The internal stresses
190
The equations of motion of an elastic medium The stresses are completely specified by six quantities
191
Media which possess gyrostatic momentum
192
The final equations of motion
194
The waves consist of two distinct types viz dilatational and distor tional waves
195
190191 Criticisms on Greens Theory
197
CHAPTER XII
198
Reflection and refraction Light polarized in the plane of in cidence
199
Change of phase
201
or surface waves
203
Greens formula show that too much light is reflected at the polarizing angle
206
Change of phase
207
Proof that the theories of Neumann and MacCullagh lead to two polarizing angles
209
Theory of Newtons rings when the angle of incidence exceeds the critical angle
210
201202 Distinction between light polarized in and light polarized perpendicularly to the plane of incidence
211
Intensity of the transmitted light
212
Black spot at the centre
213
Intensity of light reflected from a pile of plates
214
Intensity of light reflected and refracted by a single plate
215
Polarization by a pile of plates 130
217
Finely divided substances exhibit colour or are white
218
Discussion of the tables
219
Perfectly transparent plates
221
CHAPTER XIII
223
Propagation of an arbitrary disturbance
224
Poissons solution of the equation ovV
225
ART PAGE
226
Stokes application of the preceding results
232
Statement of Stokes law
238
Simple source of light
244
The colour of light depends upon the period
283
Spectrum analysis
284
Bunsen and Kirchhoffs discovery that every substance when incan descent produces its own particular spectrum
285
The infrared and ultraviolet waves
286
The ultraviolet waves are noted for their chemical effects
287
Spectrum analysis enables the presence of elements to be detected in the sun and fixed stars
288
Kirchhoffs laws of absorption
289
Spectrum analysis enables the relativo motions of the sun and fixed stars to be determined in cases where astronomical methods fail
290
298299 Huggins investigations on the proper motions of the stars
291
Selective absorption
292
Colours op natural boDies
294
DichroMatism
295
Anomalous Dispersion
296
ART FAGE 314 Selective reflection
298
Subsequently studied by Christiansen
299
Selective reflection differs from metallic reflection since the former produces strong chromatic effects
300
Kundts experiments
301
Stokes experiments on quinine
302
Stokes law 803
303
Dynamical illustration of a medium which produces fluorescence
304
CalorescenCe
305
Phosphorescence
306
CHAPTER XVII
308
Small oscillations of a sphere attached to a spring which is vibrating under the influence of waves of sound
309
338339 Discussion of the results and their application to phosphor escence
310
340341 Application to absorption
311
The experiments of Kundt show that anomalous dispersion is pro duced by most of the aniline dyes 297
312
343344 The equations of motion of the molecule and their integration
313
The equations of motion of the ether
317
Expression for the index of refraction
318
Application to anomalous dispersion
319
Discussion of the value of the index of refraction 819
320
AKT PAGE 354 Von Helmhollz theory of anomalous dispersion
321
The equations of motion of the ether and the matter
322
Integration of the equations of motion
323
Expression for the index of refraction
324
Application of the theory to anomalous dispersion
325
The theory may be extended so as to apply to a medium having several absorption bands
326
Values of the changes of phase
327
Colour of the reflected light depends upon its state of polarization
328
CHAPTER XVIII
329
The principal incidence and azimuth depend upon the medium in contact with a metallic reflector
330
Theories of metallic reflection
332
Expression for the quasirefracted wave
334
Expressions for the ratio of the amplitudes and the difference of the changes of phase
335
The constants R and a can be calculated from experiment
336
B O
337
Jamins experimental laws concerning the changes of phase
339
Eundts experiments
341
Eisenlohrs calculations For many metals the real part of ju2 must be negative
342
Metallic reflection cannot be explained by the introduction of a viscous term
343
Discussion of the results to which this theory leads
344
388389 Criticisms on the theories relating to the mutual reaction of ether and matter
345
ABT PAGE 390 Maxwells hypothesis
347
391393 Equations of the electromagnetic field
348
General equations of electric displacement for a doublyrefracting medium
349
Equations of magnetic induction
350
The disturbance which produces light is represented by the electric displacement
351
Kundts law 298
352
Magnitude and direction of the electromotive force
353
Summary of the results
354
Isotropic media
355
Maxwells concluding remarks on the theory
356
405406 Hopkinsons experiments
357
408409 Hertzs experiments
359
Experimental verification of Fresnels hypothesis with regard to the vibrations of polarized light
360
Intensity of light
361
These conditions reduce to four equations
362
Reflection and refraction at the surface of an isotropic medinm and a uniaxal crystal
363
416417 When both media are isotropic the intensities are determined by Fresnels formula
365
MacCullaghs investigations Uniradial directions
368
MacCullaghs theorem
369
Polarizing angle in the case of a uniaxal crystal whose axis lies in the plane of incidence
371
Reflection at a twin plane Stokes experiments
372
Definition of a twin crystal
373
432434 Plane of incidence perpendicular to the plane of symmetry
375
435436 In this case the direction of polarization is reversed by reflection when the angle of incidence is small
379
CHAPTER XX
380
Faradays experiments
381
Glass when under the action of electrostatic force behaves like a negative uniaxal crystal
382
Resin behaves like a positive uniaxal crystal
383
Kerrs experiments on reflection from a magnet
384
Experiments upon from a magnetic pole
385
Experimental results in this case
386
Description of the arrangements employed
387
Summary of the experimental results
388
Halls experiments on nickel and cobalt
389
Kundts experiments on magnetized glass
390
Summary of results
391
ABT PAGE 472 Table of the values of Halls effect for different metals
392
Theory of magnetic action on light
393
Equations of motion
395
Propagation of light
396
Rotatory polarization
399
The boundary conditions
400
The electrostatic and the electrokinetic energy
401
The final boundary conditions
404
Discussion of the results 40G 484 Reflection and refraction when the magnetization is parallel to the reflector
408
Concluding remarks
411

Common terms and phrases

Popular passages

Page 370 - Nicol's prism turned in any way. [Shown.] (5) The spectrum of the reflected light is frequently found to consist almost entirely of a comparatively narrow band. When the angle of incidence is increased, the band moves in the direction of increasing refrangibility, and at the same time increases rapidly in width. In many cases the reflection appears to be almost total.
Page 345 - But the properties of bodies are capable of quantitative measurement. We therefore obtain the numerical value of some property of the medium, such as the velocity with which a disturbance is propagated through it, which can be calculated from electromagnetic experiments, and also observed directly in the case of light. If it should be found that the velocity of propagation of electromagnetic disturbances is the same as...
Page 354 - The difference between these numbers is greater than can be accounted for by errors of observation, and shows that our theories of the structure of bodies must be much improved before we can deduce their optical from their electrical properties. At the same time, I think that the agreement of the numbers is such that if no greater discrepancy were found between the numbers derived from the optical and...
Page 345 - ... has independently suggested the idea of a medium and if the properties which must be attributed to the medium in order to account for electro-magnetic phenomena are of the same kind as those which we attribute to the luminiferous medium, in order to account for...
Page 370 - Some of the leading features were described as follows : — (1) If one of the crystalline plates be turned round in its own plane, without alteration of the angle of incidence, the peculiar reflection vanishes twice in a revolution, viz., when the plane of incidence coincides with the plane of symmetry of the crystal. (2) As the angle of incidence is increased, the reflected light becomes brighter, and rises in refrangibility. (3) The...
Page 104 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Page 345 - ... in the case of light. If it should be found that the velocity of propagation of electromagnetic disturbances is the same as the velocity of light, and this not only in air, but in other transparent media, we shall have strong reasons for believing that light is an electromagnetic phenomenon, and the combination of the optical with the electrical evidence will produce a conviction of the reality of the medium similar to that which we obtain, in the case of other kinds of matter, from the combined...
Page 345 - We therefore obtain the numerical value of some property of the medium, such as the velocity with which a disturbance is propagated through it, which can be calculated from electromagnetic experiments, and also observed directly in the case of light. If it should be found that the velocity of propagation of electromagnetic disturbances is the same as the velocity of light, and this not only in air, but in other...
Page 218 - ... light which is polarized perpendicularly to the plane of incidence underwent reflexion, a large part of the transmitted light polarized the other way was reflected an even number of times ; and since the length of path of the light within the absorbing medium is necessarily increased by reflexion, it follows that a defect of transparency must operate more powerfully in reducing the intensity of light polarized in, than of light polarized perpendicularly to the plane of polarization. But the Table...
Page 217 - ... substance which is at the same time finely divided, so as to present numerous reflecting surfaces, and which is of such a nature as to be transparent in mass, is brilliantly white by reflected light, — for example snow, and colourless substances thrown down as precipitates in chemical processes. The intensity of the light reflected* from a pile consisting of an infinite number of similar plates falls off rapidly with the transparency of the material of which the plates are composed, especially...

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