A Treatise On Physical Optics

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Let OP be the direction of vibration of the incident light, so that if the light is polarized by a Nicol, OP is its principal section ; and let OS be the principal section of the analyser. Let PO A = a, POS /3 ; also let the vibration which is incident upon the crystal be represented by sin 27r/T.
B On entering the crystal, the incident vibration is resolved into cos a sin 2?r^/T along OA, which constitutes the extraordinary ray, and sin a sin %7rt/r along OB, which constitutes the ordinary ray
.... The waves corre- sponding to these rays travel through the crystal with different velocities, and therefore on emergence, the two vibrations may be written ^oA ~->$3 W^. - fi. 6 ***, cos a sin 2?r (t/r Ej\) t and sin a sin 2?r (t/r 0/\) where X is the wave length in air, and and E are the thicknesses of two laminae of air, such that light would occupy the same times in traversing them, as are occupied by the ordinary and extra- ordinary waves in traversing the crystalline plate.
On entering the analyser, only those vibrations can pass through which are parallel to OS] whence resolving the two vibrations in INTENSITY OF EMERGENT LIGHT.


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