I.4 Refractive index

 

Reflection and refraction

 

 

Fig. 1.5 Reflection and refraction at the interface between air and water.

 

A ray of light hitting a surface between two isotropic media will generally give rise to a reflected ray (which never crosses the interface) and a refracted ray. The angle with which the ray hits the surface, i, will be the same as the angle of the reflected ray, r', relative to the plane perpendicular to the interface. On the other hand, when the light ray passes from one medium to another medium refraction will take place due to the differences of the speed of light in the two media (see I.1 properties of light). The relationship between the angle i of the incoming ray and the angle r of the refracted ray relative to the plane perpendicular to the interface is given by Snell's law:

 

ni sin i = nr sin r

where ni and nr are the refractive indices of the media in which the incident and refracted rays travel.

 

 

 

A light ray passing from one medium to another of higher refractive index is refracted toward the normal to the interface.
 

 

I.4.1 Estimating refractive index using relief in thin sections and solid particle samples

 

In thin sections the exact determination of the refractive index is generally impossible. However, in many cases one can estimate the refractive index of a mineral by using what is known as relief between a mineral and for example immersion oil, another mineral or the matrix in which the sample is embedded. Relief can be described as the depth of the shadows along a mineral's border, which is a relative indication of the refractive index of the mineral compared to the surrounding material. When the refractive indices are very close together the mineral becomes almost completely invisible. When the difference in refractive indices increases, the relief increases from low through moderate, high to extremely high. Extremely high relief can be characterised by the presence of very strong shadows around the mineral grains or crystals. When the refractive index of the mineral is less than that of the surrounding material we talk about negative relief, while when the refractive index is higher we talk about positive relief. To see the difference between positive and negative relief takes a lot of experience, but there are techniques to help you.


 

 

 

Table 1 Classes of relief useful for estimating refractive indices.

 

mineral

n

Relief relative to Canada balsem

nmin – ncan.

 fluorite

 ~ 1.435

 clearly negative

  ~ -0.1

 leucite

 ~ 1.510

 low negative

  ~ -0.025

 Canada balsem

 ~ 1.535

 -

  ~ 0

 quartz

 ~ 1.545 (no)

 low positive

  ~ 0.01

 apatite

 ~ 1.635 (no)

 average positive

  ~ 0.1

 augite

 ~ 1.71 (nβ)

 highly positive

  ~ 0.2

 zircon

 ~ 1.95 (no)

 very highly positive

  ~ 0.4

 rutile

 ~ 2.6 (no)

 extremely positive

  ~ 1

 

I.4.2 Determination of the refractive index relative to index liquids and other media

 

The refractive index of a crystal can be determined by embedding it in a medium with known refractive index n. The smaller the difference in refractive index the weaker the surface of the crystal will be visible. Are the refractive index of a transparent crystal and the medium nearly the same, the crystal will become nearly invisible. When a range of liquids with know refractive indices are present, one can bracked of a range of refractive indices in which the refractive index of the crystal will be:

nliq1 < nmin < nliq2

 

 By changing the index liquids one can minimise the range. The amount of visibility of the crystal is known as relief. There are two methods to determine whether the refractive index of a mineral is higher or lower than that of the index liquid or other media.

 

The Becke line method (Fig. 1.6)

 

For this method the diaphragm needs to be fully closed. When the crystal is completely in focus, light from the surface of the crystal will be seen exactly on the crystal surface in the image and will therefore not be visible. However, when we lower or turn up the stage, the refracted light beam will no longer coincide with the crystal surface in the image, but will become visible as a small line just next to the surface. This is known as the Becke line. Now one can distinguish two possibilities:

1)      lowering stage (Fig. 1.6b): Becke line moves into medium with highest refractive index

2)      turning up stagebecke: Becke line moves into medium with lowest refractive index

 

 

Fig. 1.6a Rays 1 and 2 refracted toward the normal of the interface in the media of higher n, Ray 3 is reflected at the interface, and Ray 4 is refracted away from the normal of the interface in the media of lower n.

Fig. 1.6b The formation and movement of the Becke line as function of refractive index.

 

Oblique illumination method or Schroeder van der Kolk method (Fig. 1.7)

 

This method is mainly used in powder samples. It is based on bringing in a shadow in the light beam above the objective, for example by partially bringing in the gypsum plate. This blocks of a part of the field of view, while in the remaining part the particles will show a shadow side. When the refractive index of the mineral is higher than that of the index liquid, then the shadow will be visible on the side where the field of view is blocked. Is the refractive index lower, then the shadow will appear on the opposite side. This can be explained by assuming that the particle is acting as a small lens. This lens is positive when the refractive index of the particle is higher and negative when the refractive index is lower.

 

 

Fig. 1.7 the oblique illumination method

 

I.4.3 Dispersion of light: coloured Becke lines

 

When the refractive index of a mineral is close to the refractive index of the surrounding material, the Becke lines (as well as the bright and shadowed areas in the oblique illumination method) will show distinctive colours, when white light was used to illuminate the mineral. This is caused by dispersion of the white light at the grain boundary into its spectrum (like what happens in a prism). Because the speed of light in a material depends on its wavelength, also the refractive index depends on the wavelength. In general the refractive index for colours with a larger wavelength (red side of the spectrum) is smaller than for colours with smaller wavelengths (blue side of the spectrum). Observation of these dispersion colours can help to determine whether the refractive index of a mineral grain or crystal is smaller or larger than the medium around it.

 

The wavelength of light is generally given in the notation of Fraunhofer lines of the solar spectrum (dark lines due to the absence of specific wavelengths in sunlight due to absorption). The mostly used notations are:

 

  Line element wavelength
red C H 656.3 nm
yellow D1 Na 589.6 nm
  D2 Na 589.0 nm
blue F H 486.1 nm

 

For accurate measurements one normally reports nD, unless otherwise mentioned. The dispersion is then given as:

 

nF - nC, or as (nF-nC)/nD

 

Immersion liquids have in general a stronger dispersion than crystals, especially for liquids with a refractive index higher than 1.6. Here one will see coloured Becke lines, when the mineral has a higher refractive index in the red part of the spectrum and a smaller refractive index in the blue part of the spectrum in comparison to the surrounding liquid. In this case, when one lowers the microscope stage, a red or yellow line will move into the mineral, while a green or blue line will move into the liquid. Are the Becke lines green or red, then the refractive index nD of the mineral is about the same as that of the immersion liquid. Are the lines blue or yellow then the refractive index nD (roughly similar to the behaviour of the yellow Becke line) of the mineral is slightly higher.