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Double Refraction

Erasmus Bartholinus discovered, in 1669, that when a ray of light is refracted by a crystal of calcite it gives two refracted rays. This phenomenon is called double refraction. Calcite or Iceland spar is crystallized calcium carbonate (CaCO₃) and was found in large quantities in Iceland as very large transparent crystals. Due to this reason calcite is also known as Iceland spar. It crystallizes in many forms and can be reduced by cleavage or breakage into a rhombohedron, bounded by six parallelograms with the angles equal to 102˚ and 78˚ (more accurately 101˚ 55’ and 78˚ 5’).

Optic axis: At two opposite corners A and H, of the rhombohedron all the angles of the faces are obtuse. These corners A and H are known as the blunt corners of the crystal. A line drawn through A making equal angles with each of the three edges gives the direction of the optic axis. In fact any line parallel to this line is also an optic axis. Therefore optic axis is not a line but it is a direction. Moreover, it is not defined by joining the two blunt corners A and H coincides with the crystallographic axis of the crystal and it gives the direction of the optic axis. If a ray of light is incident along the optic axis or in a direction parallel to the optic axis, then it will not break into two rays. Thus, the phenomenon of double refraction is absent when light is allowed to enter the crystal along the optic axis.

The phenomenon of double refraction can be shown with the help of the following experiment:

Mark an ink dot on a piece of paper. Place a calcite crystal over this dot on the paper. Two images will be observed. Now rotate the crystal slowly as shown in fig. Place your eye vertically above the crystal. It is found that one image remains stationary and the second image rotates with the rotation of the crystal. The stationary image is known as the ordinary image while the second one is known as the extraordinary image.

When a ray of light AB is incident on the calcite crystal making an angle of incidence = i, it is refracted along two paths inside the crystal, (i) BC making an angle of refraction = r₂ and (ii) along BD making an angle of refraction = r₁. These two rays emerge out along DO and CE which are parallel.

The ordinary ray has a refractive index = sin i/sin r₁ and the extraordinary ray has a refractive index = sin i/sin r₂. It is found that the ordinary ray obeys the laws of refraction and its refractive index is constant. In the case of the extraordinary ray, its refractive index varies with the angle with the angle of incidence.

It has been found that both the rays are plane-polarized. The vibrations of the ordinary ray are perpendicular to the principal section of the crystal while the vibrations of the extraordinary ray are in the plane of the principal section of the crystal. Thus, the two rays are plane polarized, their vibrations being at right angles to each other.

Special cases: (1) It should be remembered that a ray of light is not split up into ordinary and extraordinary components when it is incident on calcite parallel to its optic axis. In this case, the ordinary and the extraordinary rays travel along the same direction with the same velocity.

(2) When a rays of light is incident perpendicular to the optic axis on the calcite crystal, the ray of light is not split up into ordinary and extraordinary components. It means that the ordinary and extraordinary rays travel in the same direction.