Index of Refraction

The index of refraction (n) quantifies how strongly a material slows light. It is defined as the ratio of the velocity of light in a vacuum (Vv) to the velocity of light in the material (Vm). ^[1]

Because light always travels faster in a vacuum than in any material, n is always greater than 1. A higher n means the material slows light more strongly, which has direct consequences for reflection, refraction, and luster.

Reflection and Refraction at a Boundary

When light reaches the surface of a mineral, some of it is reflected and some is refracted into the mineral. For reflected light, the angle of incidence and the angle of reflection are identical (both measured from the normal to the surface). Light that enters the mineral at any angle other than normal is bent, or refracted - this is refraction.

The angle of refraction is determined by Snell’s law, which relates the indices of refraction of the two materials (n₁, n₂) to the angles (θ₁, θ₂) between the wave normals and the surface normal: sin θ₁ / sin θ₂ = n₂ / n₁. Snell’s law holds for both isotropic and anisotropic materials, provided the angles are measured using the wave normal directions, not the ray paths - in anisotropic materials these two diverge, but the wave normal governs the wave front behavior described by the law. ^[1]

Index of Refraction, Reflectance, and Luster

Both the index of refraction and the angle of incidence control how much light is reflected from a mineral’s surface versus transmitted into it. Reflectance increases with a higher index of refraction. For a material with n = 1.55 - window glass - light striking normal to the surface (angle of incidence = 0°) is only about 5% reflected, allowing 95% of the light to enter. The minimum reflectance needed to produce a perceived metallic luster, which requires more than 20% reflectance at normal incidence, demands an index of refraction greater than 2.6. ^[1]

Angle of incidence also matters. At very shallow angles (θ₁ close to 90°), most of the light is reflected regardless of the mineral’s index of refraction. This is why the surface of any smooth mineral looks mirror-like when viewed at a glancing angle.

Critical Angle and Total Internal Reflection

Light can always travel from a low-index material into a high-index material - the angle of refraction is simply smaller than the angle of incidence. The reverse - traveling from high-index to low-index - has a limit. The critical angle (CA) is the angle of incidence at which the refracted ray would travel exactly along the interface (angle of refraction = 90°). Any light hitting the boundary at an angle greater than the critical angle cannot enter the low-index material at all: it undergoes total internal reflection, meaning all light bounces back into the high-index material. ^[1]

The critical angle is calculated from the indices of the two materials using the expression sin CA = n₂(low) / n₁(high). Total internal reflection is the basis of refractometry, the technique used to measure mineral refractive indices in grain mounts.

Normal Dispersion of Refractive Indices

In most transparent minerals, violet light is refracted more strongly than red light - that is, the index of refraction is higher for shorter wavelengths and lower for longer wavelengths. This relationship is called normal dispersion of the refractive indices. By convention, indices are reported at three specific wavelengths corresponding to Fraunhofer absorption lines in the solar spectrum: n_F at 486 nm, n_D at 589 nm, and n_C at 656 nm. These wavelengths are chosen because they are easily reproduced in the laboratory. ^[1]

The practical effect of normal dispersion is that white light is spread into its component colors when refracted - the same principle that produces a rainbow and the prismatic flashes visible in high-n minerals in thin section.

The Standard nD Value

When a single index of refraction is reported for a material without further qualification, it is always n_D - the index measured at 589 nm. This wavelength was chosen because it falls in the middle of the visible spectrum and is readily produced by a sodium vapor lamp in the laboratory. ^[1]

Strongly colored minerals may show abnormal dispersion, in which the index of refraction actually increases with increasing wavelength for wavelengths that are heavily absorbed by the mineral. This is the opposite of the normal trend and is caused by absorption band effects.

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