The Analytical Theory of Light
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The planes of polarisation of the two refracted waves are at right-angles, only when cos #2 = 0, cos < e = 0, sin (r e r ) = 0, that is when the optic axis is either in the plane of incidence or parallel to the extraordinary wave, and when the two refracted waves have the same direction, that is in the case of normal incidence. 120, 121] Fresnel's Investigations 195 Biaxal Crystals, 121. The first attempt to extend Huygens' construction to biaxal crystals was made by Young*, who suggested a sphere combined with an ellipsoid having three unequal axes as the form of the wave-surface in such media. It is readily seen however that this form of wave-surface is inconsistent with the biaxal character of the crystals, and in addition Fresnel discovered that' any form with a spherical sheet must be rejected, since in biaxal crystals there is no ordinary refraction in all cases, as was at first supposed to be the case. Fresnel arrived at this conclusion by the following considerations. Starting from the idea that light consists in transverse vibrations of the particles of the ether, he was led by the symmetry of uniaxal crystals about their axis to assume that vibrations perpendicular to this direction are propagated with the same speed in all directions f, and he pointed out that this explains the existence of an ordinary wave and the relation between its velocity and that of the extraordinary wave, provided the vibrations in a stream of polarised light are perpendicular to the plane of polarisation : for in that case, light polarised in the principal plane will travel with the same speed in all directions, as the vibrations are in all cases perpendicular to the optic axis ; on the other hand light polarised in a plane perpendicular to the principal plane will have a speed dependent upon the direction of propagation, as the vibrations are in general oblique to the optic axis.
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To quickly assess the difficulty of the text, read a short excerpt:
The planes of polarisation of the two refracted waves are at right-angles, only when cos #2 = 0, cos < e = 0, sin (r e r ) = 0, that is when the optic axis is either in the plane of incidence or parallel to the extraordinary wave, and when the two refracted waves have the same direction, that is in the case of normal incidence. 120, 121] Fresnel's Investigations 195 Biaxal Crystals, 121. The first attempt to extend Huygens' construction to biaxal crystals was made by Young*, who suggested a sphere combined with an ellipsoid having three unequal axes as the form of the wave-surface in such media. It is readily seen however that this form of wave-surface is inconsistent with the biaxal character of the crystals, and in addition Fresnel discovered that' any form with a spherical sheet must be rejected, since in biaxal crystals there is no ordinary refraction in all cases, as was at first supposed to be the case. Fresnel arrived at this conclusion by the following considerations. Starting from the idea that light consists in transverse vibrations of the particles of the ether, he was led by the symmetry of uniaxal crystals about their axis to assume that vibrations perpendicular to this direction are propagated with the same speed in all directions f, and he pointed out that this explains the existence of an ordinary wave and the relation between its velocity and that of the extraordinary wave, provided the vibrations in a stream of polarised light are perpendicular to the plane of polarisation : for in that case, light polarised in the principal plane will travel with the same speed in all directions, as the vibrations are in all cases perpendicular to the optic axis ; on the other hand light polarised in a plane perpendicular to the principal plane will have a speed dependent upon the direction of propagation, as the vibrations are in general oblique to the optic axis.
What to read after The Analytical Theory of Light?
You can find similar books in the "Read Also" column, or choose other free books by Walker, James, 1794-1874 to read online
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