Double Refraction

Double refraction is the defining optical behavior of anisotropic minerals. When light enters an anisotropic mineral in most directions, it is split into two separate rays that travel at different velocities and vibrate at right angles to each other. This splitting arises because the electronic environment of the crystal structure varies with direction, causing light velocity to vary as well. ^[1]

The Calcite Demonstration

Double refraction can be seen directly with the naked eye using a cleavage rhomb of clear calcite. When the rhomb is placed over a mark on a piece of paper, two separate images of the mark appear. Viewing the rhomb through a piece of polarizing film demonstrates that the two rays are plane-polarized: when the film’s vibration direction is parallel to the short diagonal of the rhomb, only one image is visible; rotate the film by 90° and only the other image survives. The two rays must therefore be plane-polarized and vibrating at exactly right angles to one another. ^[1]

Fast Ray and Slow Ray

The two rays produced by double refraction do not travel at the same speed. Measuring their respective indices of refraction reveals that one ray moves faster than the other. The ray with the lower index of refraction - and therefore the greater velocity - is called the fast ray. The ray with the higher index of refraction - and therefore the lower velocity - is called the slow ray. ^[1]

This velocity difference is what makes double refraction optically useful. As the two rays travel through a mineral plate of thickness d, the slow ray progressively falls further and further behind the fast ray. The gap that accumulates between them by the time both rays exit the mineral is called the retardation.

Retardation and Birefringence

When plane-polarized light from the lower polarizer enters an anisotropic mineral, it splits into the slow and fast rays. In the time it takes the slow ray to travel through the mineral, the fast ray travels through the mineral plus an additional distance Δ, the retardation. Once both rays exit into air, they travel at the same velocity again, so the retardation remains fixed. The retardation depends on the thickness of the mineral (d) and on the difference in refractive index between the slow ray (n_s) and fast ray (n_f): ^[1]

The term δ = n_s − n_f is the birefringence of the mineral in that direction. The numerical value of birefringence is not constant for a given mineral - it depends on the direction the light follows through the crystal. Along an optic axis the birefringence is zero; in other orientations it takes on intermediate values up to a characteristic maximum. This maximum birefringence is a useful diagnostic property for mineral identification, because it determines the highest interference color a particular mineral can produce in thin section.

Optic Axes and Optical Categories

Every anisotropic mineral has at least one special direction, called an optic axis, along which light is not split into two rays. Along this direction, the section through the optical indicatrix is circular, birefringence is zero, and the mineral behaves as if it were isotropic. ^[1]

The number of optic axes divides anisotropic minerals into two categories: ^[1]

• Uniaxial minerals have one optic axis. These belong to the hexagonal and tetragonal crystal systems, which have a single c axis of high rotational symmetry. ^[1]
• Biaxial minerals have two optic axes. These belong to the orthorhombic, monoclinic, and triclinic crystal systems, which lack a single high-symmetry axis. ^[1]

Uniaxial and biaxial are the two fundamental categories of optical character for anisotropic minerals.

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