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When a ray of light enters from one medium to another medium, it deviates from its path either toward or away from the normal obeying Snell’s law. If medium is isotropic, refraction takes place only in one direction, whereas in case of anisotropic medium, Erasmus Bartholinus in 1669 discovered that the refraction is not confined to single direction. He found that when a ray of ordinary light is incident on calcite or quartz crystals, it splits up into two polarized refracted rays. This phenomenon is called double refraction and crystal is known as doubly refracting crystals. The phenomenon of double refraction can be explained by a simple experiment. Mark an ink dot on a piece of paper and place a calcite crystal over this dot. Two images of ink mark will be observed. On rotating the calcite crystal either clockwise or anti-clockwise, it is found that one image rotates with the rotation of crystal and other image remains stationary as shown in Figure 6.7. The stationary image is known as ordinary image and rotating image is known as extraordinary image. The refracted ray which produces ordinary image is known as 0-ray i.e., ordinary rays and obey ordinary laws of refraction, and the refracted ray which produces extraordinary image is known as extraordinary ray (E-ray) and does not obeys ordinary laws of refraction

Consider a narrow beam of light PQ incident on a calcite crystal making an angle i with the normal, it is refracted along two directions QR and QS at angles r 1 and r 2 respectively, as shown in Figure 6.7(b). These two rays finally emerges as 0-ray and E-ray which are parallel to each other as well as parallel to direction of incident beam.


For O –ray , µO =sin i/sin r l


For E-ray  , µE =sin I /sinr2


As r1 < r2 there µ o > µ o < µE. This is because

µ =sin i /sin r = Velocity of light in air / Velocity of light in medium vair/vmed


Birefringence: The difference between refractive index for 0-Ray and E-Ray is called birefringence i.e.,


µ0 = µE = birefringence


Thus in case of calcite crystal the velocity 0-ray is less than that of E-Ray i.e., in crystal of calcite extraordinary ray travels faster than that of ordinary ray. Further it has been found that, for 0-ray, the refractive index is same for all angle of incidence whereas for E-ray, the refractive index is different for different angle of incidence. Thus 0-ray travels with same speed in all  direction whereas E-ray travels with different speed in different directions.


It has been observed that both 0-ray and E-ray are plane polarised. The vibrations of ordinary ray are perpendicular to principal section of the crystal and vibrations of extraordinary

ray are along the principal section of the crystal.


(a) Geometry of Calcite Crystal


The calcite crystal, also known as Iceland spar (CaC03) is a colourless crystal, transparent to visible as well as to ultraviolet light. It is available in different shapes and can be easily reduced to rhombohedron bounded by six parallelograms with angle 102° and 78° as shown in Figure 6.8(a). At comers A and Hall the faces make equal obtuse angles, are known as blunt corners. A line passing through one of the blunt comers and is equally inclined to all the three edges meeting over there gives the direction of optic axis. Any line parallel to this line is also known as optic axis.


A line joining two opposite blunt comers is not an optic axis, but only in case of cubic

crystal where all the three edges are equal, a line joining two opposite blunt comers will be an

optic axis.



(1)  When a ray of light is incident along optic axis, then it is not doubly refracted, because in this case both 0-ray and E-ray travels along the same direction with same velocities.


(ii) When a ray of light incident perpendicular to optic axis is not doubly refracted because in    this case 0-ray and E-ray travels along the same direction but with different velocities.


(b) Principal Section of the Crystal


A plane containing optic axis and perpendicular to the opposite faces of the crystal is called principal section of the crystal. As there are six faces in a crystal so for every point, there

are three principal sections passing through any point inside the crystal, one corresponding to each pair of opposite faces. A principal section always cuts the surface of calcite crystal in

parallelogram with angles 109° and 71°.

(c) Principal Plane of the Crystal


For ordinary ray, principal plane is the plane drawn through optic axis and ordinary

ray and for extraordinary ray, principal plane is the plane drawn through optic axjs and extraordinary ray. The ordinary ray always lie in the plane of incidence, whereas for extraordinary ray this is not generally true. The incidence plane of two rays do not coincide . but in particular case, when the plane of incidence is a principal section then principal section of crystal and principal planes of ordinary and extraordinary rays coincide.


 (d) Types of Crystal


Uniaxial Crystals: Those crystals in which there is a single direCtion called optic axis along which 0-rays and £-rays are transmitted with same velocity and along any other direction they have different velocities are called uniaxial crystal e.g., calcite, quartz, tourmaline etc.


Biaxial Crystals: Those crystals in which there are two directions along which 0-rays and £-rays are transmitted with same velocity (i.e., they have more than one optic axis) are called biaxial crystals e.g., borax, mica, topaz etc.