130 REPORT ON PHYSICAL OPTICS. 



ciently thin such as the laminae into which mica or sulphate of 

 lime may be readily divided by cleavage, the most gorgeous 

 colours appear, which vary with every change of inclination of the 

 plate to the polarized beam. When the plate is perpendicular 

 to the transmitted pencil, and then turned round in its own 

 plane, the tint does not change, but only varies in intensity, 

 being a maximum when the principal section of the crystal is 

 inclined at an angle of 45 to the plane of primitive polariza- 

 tion, and vanishing altogether when it coincides with that plane, 

 or is perpendicular to it. On the other hand, when the crys- 

 tal is fixed, and the analyzing plate turned, so as to vary the 

 inclination of the plane of the second reflexion to that of the 

 first, the colours change in the most striking manner ; and it 

 is found that the colour reflected, in any one position of the 

 plane of the second reflexion, is always complementary to that 

 reflected in the perpendicular position. The colours disappear 

 altogether when the thickness of the crystalline plate is reduced 

 below a certain limit.* 



The experimental laws of these phenomena were investigated 

 with unwearied zeal by M. Biot.f When the light was inci- 

 dent perpendicularly on plates of the same substance, of different 

 thicknesses, the tints were observed to follow the same law 

 as the colours of thin plates ; the thicknesses of the crystal at 

 which each tint was developed in perfection being proportional 

 to the thicknesses of the plate of air which gave the same tint in 

 Xewton's scale. These thicknesses vary with the nature of the 

 crystal, and are always much greater than the corresponding 

 thicknesses of the uncrystallized plate which exhibit the same 

 tint. Pursuing the same inquiry, afterwards, for oblique inci- 

 dences, M. Biot found that, in uniaxal crystals, the tint de- 

 veloped was determined by the length of the path traversed by 

 the light within the crystal, and by the square of the sine of the 

 angle which its direction made with the optic axis, jointly. 

 From this law it followed, that if a crystalline plate of moderate 

 thickness be cut perpendicularly to the axis, and a converging 

 or diverging pencil transmitted through it, the lines of equal 

 tint or the isochromatic lines, as they are sometimes called, 

 will be disposed in concentric circles similar to Newton's rings. 



* Him. Int. 1811. t nid ^ I8i2 . 



