Artists are sometimes surprised to see one application of paint barely hide the drawing or painting underneath, and another color completely mask all that was below. Some wonder why sometime after they completed a painting, they begin to see lines of the sketch that before were completely unnoticed. (This effect is called pentimento.) Other artists wishing to apply a beautiful glaze are frustrated when the glaze kills the color below. These are common problems experienced by all painters at one time or another, but the reasons are little understood by them.

Given the same thickness of applied paint film, not all paints are equally opaque (or transparent). We call this hiding strength or covering power. The hiding strength (or opacity) of paint is largely influenced by the difference of the refractive indices of the pigment and the medium, particle size and dispersion of the pigment (i.e. particle shape and degree of aggregation of the particles), the proportion of pigment in the vehicle (i.e., pigment volume concentration or PVC) and the thickness of the applied film. These factors determine the opacity of a particular paint. In this article, we will focus on the refractive index of pigments and paint vehicles; the other factors were considered in another article, "Do Natural Pigments Offer More to the Modern Painter?"

Paints are materials containing tiny pigment particles suspended in a binder, such as oil. We are accustomed to regard some pigments as transparent, or translucent, and others as opaque. Pigments usually considered to be opaque are translucent in a highly refractive medium. Using a medium of high refractive index, it can be shown that the most opaque colors, even lead white, appear transparent. This demonstrates that the hiding strength or opacity of a pigment can be lost through a change in the conditions that surround the pigment, or in the case of paint, a change in the binder.

Pigment particles absorb certain wavelengths of light, creating colored paints, or they may reflect, refract and scatter all wavelengths of light, appearing white to our eyes. Lets consider what happens when light encounters a layer of paint containing only pigment particles.

The Behavior of Light Passing Through Substances

To help us understand the opacity of pigment in paint, we will need to consider the behavior of white light on substances. We think of a sheet of glass as a transparent substance through which light passes without obstruction. Yet, if we look out of our window at night we get a nearly perfect mirror image of the interior of our home.

As beams of light pass from the air to glass they are impeded, so that some light is reflected while parts are transmitted. If the beam of light, called incident light, hits the glass at an angle, the transmitted beam is bent out of its path on entering the glass so as to shorten its path (fig.1).

Fig. 1. When light passes through a substance some of it is reflected and some transmitted. Transmitted light is refracted as it encounters a material, such as liquid or solid that impedes it velocity through it.

Light travels at a constant velocity in a vacuum, but when it travels through a substance its velocity is slower. So, in our example, when the light passes from less dense air to denser glass, its velocity is slowed down; the beam of light is bent or refracted. The amount of refraction is the measure of impediment given by the substance to the beam of light. In our example, we can substitute the glass for other substances, such as water, oil, or pigments, and find the amount light is impeded is different for each substance. (The degree to which light is bent is also dependent upon other factors, such as the temperature of the substance and the wavelength of the light.) The proportion between the light that is reflected and the light that enters the substance and is refracted also varies.

The ratio of the velocity of light in a vacuum to the velocity of light in another substance is expressed as the index of refraction or refractive index. It is measured by the angle at which the ray of light is bent. To determine this ratio, one must know the angle of incidence, or the angle between the ray of light entering the substance and a line perpendicular to its surface, and the angle of refraction, defined as the angle between the refracted ray and the perpendicular to the surface. In mathematical terms, if i is the angle of incidence and r is the angle of refraction, then the refractive index is N, expressed as follows:

   sine i
N =  -------
   sine r

By definition the refractive index of a vacuum is 1. In practice, air makes little difference to the refraction of light with an absolute refractive index of 1.0008, so the value of the absolute refractive index can be used assuming the incident light is in air. Since light slows down when it enters a substance, so the refractive index will always be greater than 1. Most minerals have refractive indices between 1.32 and 2.40, with values between 1.50 and 1.80 (Jones, 1980).

Material Refractive Index
Air 1.0008
Water 1.3330
Glass, soda-lime 1.5100
Ruby 1.7600
Diamond 2.4170

The amount light rays may be bent as shown in Figure 1, depends upon the substance it enters. This change in direction becomes smaller as the angle of incidence decreases. Eventually, when light is perpendicular to a surface it will not bend. The angles at which light is refracted is a constant. For a pigment, the constant N (refractive index) depends on the difference between the velocity of light in the surrounding medium and the pigment. It is a characteristic constant for every material including gases, liquids and solids. We cannot observe the change in the velocity of light in small pigment particles, but we can observe a change in the direction of propagation of the light and calculate or estimate the refractive index.

The refractive index is an easy concept to learn, but things aren’t quite that simple. The refractive index of a pigment particle is not necessarily the same in all directions. Most pigments are composed of crystals that have definite shapes and are classified into different systems. In cubic crystals, light travels at the same speed in all directions within the crystal, which is said to be isotropic. Light does not travel at the same speed in all directions within substances that belong to the five other crystal classes; these are said to be anisotropic. In addition, anisotropic substances are divisible into two types:

Uniaxial are substances that have two refractive indices (tetragonal and hexagonal system minerals);

Biaxial are substances characterized by three refractive indices (triclinic, monoclinic and orthorhombic system minerals).

The most important thing to remember is that a substance that has a higher refractive index is a substance that impedes the velocity of light or offers more resistance to it, and therefore a larger proportion of the light will be scattered.

Let’s return to our example of the beam of light passing into a substance. Consider what happens when a light beam is passing from a substance of one refractive index to another substance of another refractive index.

If a beam of light passes from a substance like air with a low refractive index to a substance of higher refractive index, such as water that impedes the passage of light, part of the light will be reflected at the interface or boundary of the two substances (Fig. 1). Light changes speed as it moves from air to water, so that it also experiences refraction. In our consideration of pigments, refraction is most important. If we view water inside a shallow glass dish some of the light passing through the water and entering the glass, which has a higher refractive index than water, is reflected and some refracted (Fig. 2). We get two reflections and two refractions; one at the surface of the water, and another at the boundary of the water and glass.

Fig. 2. Light passing through two substances, one of low refractive index and the other of high refractive index.

Typically, solid substances have higher refractive indices than liquids, so if we suspend a sheet of glass in a shallow dish of water, we will see a strong reflection and high refraction at their interface, because of the differences in their refractive indices (Fig. 3).

Now instead of a sheet of glass of higher refractive value than water, we place a transparent sheet of another material with a low refractive index, like gelatin; we shall get a comparably feeble reflection at the boundary of the water and gelatin.

If instead of removing the glass we replace the water with a liquid of higher refractive index, the same refractive index as glass, there will be no reflected light at the meeting of the liquid and glass.

Fig. 3. Light passing through a liquid of low refractive index and then through a glass plate, illustrating how pigment particles reflect and transmit light in a medium.

Let us summarize what we’ve learned about the behavior of light. When a ray of light is passing from a substance of low refractive index to a substance of high refractive index, light is reflected at the boundary; the amount of light scattered being greater the greater the difference between their respective refractive indices.

The Behavior of Light in Paint

Now we will approximate the conditions we find in paint. Let us return to our example of the glass sheet suspended in liquid. We now break the glass into pieces and grind it into a fine powder. This powder appears white and opaque, but if we were to examine a particle of the glass in a microscope we would see that is transparent. The reason is that the light reflected from the many of facets pf glass particles is scattered, and it is scattered light that produces opacity.

Now put the powdered glass in a container, and fill the container with water. The differences between the refractive indices of water and glass is not as great as between air and glass. As you fill the container with water, the powder glass does not scatter so much light. It becomes partly translucent. If the liquid had the same refractive index as glass, the glass would be almost invisible. Though the water is not of so high refractive index as glass, it is very much higher than air, and as we see the glass by scattered reflection, if the reflection no longer takes place, the glass disappears. This is the same phenomenon we observe when we wet an opaque substance, it appears darker in color.

We will repeat what was said earlier: Some pigments we consider to be transparent, or translucent, and others opaque. Pigments usually considered to be opaque are actually transparent in a highly refractive medium. Using a medium of high refractive index it can be shown that the most opaque colors, even lead white, appear transparent.

Most of the light enters the paint surface and then passes through the randomly shaped and oriented pigment particles. These particles are translucent and don’t absorb much light, but they have a refractive index higher than the medium that surrounds them.

What happens to the light as it passes through one of these pigment particles? A portion of the light reflects at the surface of each pigment particle. Again, changes in the speed of light as it enters the pigment particle causes the light to bend or refract. The light is impeded trying to pass through the particles, even though the particles may not absorb much light. The light’s path changes at the surface and some of it is reflected back out of the paint.

The random shape and orientation of the pigment particles are what gives a paint film of white pigment its white appearance. If all of the pigment particles were instead flat disks that lay parallel to the paints surface, like coins lying flat on the bottom of a shallow pan of water, the paint would reflect the light much like a mirror rather than form a white surface. The reason is that the flat disks would reflect light directly back from the paint in the manner as a mirror. The paint film would appear like a mirror rather than the color we perceive as white. The random surfaces of the pigment particles are what give white paint its diffuse glow. A narrow beam of light hitting white paint scatters in all directions while a beam of light hitting the mirror bounces back as a narrow beam.

If the pigment particles had exactly the same index of refraction as the medium that holds them, how would this alter the appearance of the paint? The paint would appear translucent. Without changes in the refractive index between the pigment and the medium, light passes through it practically unaffected. Although some light will reflect at the boundary of the air and paint layer, whatever light actually enters the paint will continue on all the way through it to the ground under the paint. The paint will appear translucent. Some pigments, such as chalk, when mixed with linseed oil loose their hiding strength and appear translucent, because they have a refractive index close to that of linseed oil.

White pigments typically are substances that have a refractive index above 2—a high ability to refract light that strikes it obliquely, and a high ability to reflect light. IN artists paints, there are only a few white pigments with refractive indices above 2: titanium dioxide (TiO2), lead white (basic lead carbonate, 2PbCO3•Pb(OH)2), zinc oxide (ZnO) and zinc sulfide (ZnS). On the other hand, there are many white pigments that have refractive indices less than 2 and in oil and acrylic paint are considered to be extender or filler pigments. Common ones are silica (SiO2), chalk (calcium carbonate, CaCO3), barite (barium sulfate, BaSO4), and gypsum (calcium sulfate hemihydrate, CaSO4•0.5H2O). If you look at the table of refractive indices, substances that have higher refractive indices have greater opacity or covering power because of their high refractive index.

Refractive Indices of Various Pigments
Color Pigment Refractive Index
Blues Azurite 1.73–1.84
Indigo (natural dye) 1.49–1.52
Smalt 1.49–1.52
Lazurite (natural ultramarine) 1.50
Vivianite (blue ocher) 1.58–1.70
Greens Chrysocolla 1.58–1.60
Dioptase 1.64–1.71
Glauconite (green earth) 1.62
Malachite 1.65–1.90
Verdigris (basic copper acetate) 1.53–1.56
Volkonskoite 2.50
Yellows Gamboge (organic resin) 1.58–1.59
Indian yellow (organic resin) 1.67
Jarosite 1.71–1.82
Massicot (litharge, lead monoxide) 2.50–2.61
Goethite (yellow ocher) 2.00–2.40
Orpiment 2.40–3.02
Reds Cinnabar 2.81–3.15
Hematite (red iron oxide) 2.78–3.01
Realgar 2.46–2.61
Red lead (minium or lead tetroxide) 2.42
Vermilion 2.82–3.15
Browns Goethite (brown ocher) 2.08–2.40
Siderite 1.57–1.78
Sienna, burnt 1.85
Sienna, raw 1.87–2.17
Umber, burnt 2.20–2.30
Umber, raw 1.87–2.17
Whites Chalk (whiting, calcium carbonate) 1.51–1.65
Gypsum, anhydrite (calcium sulfate anhydrate) 1.57–1.61
Gypsum, hemihydrate (gesso, calcium sulfate hemihydrate) 1.52–1.53
Titanium dioxide (anatase) 2.27
Titanium dioxide (rutile) 2.71
Lead white (basic lead carbonate) 1.94–2.09
Zinc oxide 2.00–2.02
Blacks Carbon black (opaque)

Since for white pigments there is little or no absorption of light, the hiding power of white paints depends entirely on the scattering of the incident light. The higher the refractive index of the pigment relative to that of the medium and the nearer the particle size to the optimum, the greater the scatter and the greater the opacity of the paint.

The hiding power of a paint containing a colored pigment is also dependent on the ability of the pigment to absorb light, as well as to scatter it as a result of its refractive index and particle size distribution. With black pigments good hiding power is obtained owing to the almost complete absorption of light and refractive index as such contributes only little to the effect. For other colored pigments both of these properties, absorption and scatter, are wavelength dependent and the end effect is a complex combination of all the various factors involved.

All inorganic pigments have high refractive indices, and hence, when used to color paint give high opacity. Such colors from inorganic pigments generally include white, black, and yellow, red and green oxides. Colors comprising combinations of inorganic and organic pigments may have high opacity, depending on the proportions.

Changing Opacity of Oil Paint

The Miracles of Saint Francis of Paola by Peter Paul Rubens

Peter Paul Rubens, The Miracles of Saint Francis of Paola, oil on panel, 975×772 mm, c. 1627–8, J. Paul Getty Museum. Click on the image to see a detail of the pentimento.

The refractive index of substances is not absolute, but changes with time. For example, as linseed oil ages, the refractive index increases from 1.479 to over 1.525 in about ten years. It has been measured as high as 1.58 in paintings several hundred years old. This causes oil paint to loose it’s covering power and become more transparent with time. This phenomenon can be seen in such old masters paintings as the pentimento in the upper left of Peter Paul Rubens’ modello The Miracles of Saint Francis of Paola. The two columns appear superimposed on top of an archway. The archway was painted over, but it reappeared as the painting aged and the layers of oil paint became transparent.

To avoid this effect artists must be aware of the changes in refractive index and use pigments with high refractive indices and apply sufficiently thick layers of paint.

Conclusion

When selecting a pigment it is important to know how opaque it is in the paint binder. Depending upon the desired effect of the paint, such as scumbles or glazes, you will need to use either opaque or transparent pigments. For underpainting, you will normally need an opaque pigment, and for the final layers, one with a lower refractive index. The opacity of a pigment depends largely on the difference between the refractive indices of the pigment and the binding materials, on the granularity of the pigments and the degree of pigment concentration in the binding medium.


Appendix

Refractive Indices of Common Artist’s Paint Resins and Binders
Material Refractive Index
Water 1.333
Linseed oil, refined, fresh* 1.479
Linseed oil, aged 10 years >1.520
Egg yolk, dried 1.525
Artificial Resins
Polyvinyl acetate (PVA) 1.473
Acrylic (methyl methacrylate) 1.489–1.498
Acrylic copolymer (methyl methacrylate styrene) 1.558–1.574
Natural Resins
Damar, Singapore
1.515
Rosin, wood, Grade M 1.525
Rosin, ester 1.496
Shellac, bleached 1.534
Mastic 1.536
Canada balsam 1.530–1.540
Sandarac 1.545

* It is well known that the refractive index, viscosity and molecular weight of linseed oil and other nonconjugated oils incease as a result of heat processing.

Source: (Gardner 1972)

Refractive indices of various blue pigments

Fig. 4. Refractive indices of various blue pigments compared to aqueous and drying oil mediums.

Refractive indices of various brown pigments

Fig. 5. Refractive indices of various brown pigments compared to aqueous and drying oil mediums.

Refractive indices of various green pigments

Fig. 6. Refractive indices of various green pigments compared to aqueous and drying oil mediums.

Refractive indices of various red pigments

Fig. 7. Refractive indices of various red pigments compared to aqueous and drying oil mediums.

Refractive indices of various white pigments

Fig. 8. Refractive indices of various white pigments compared to aqueous and drying oil mediums.

Refractive indices of various yellow pigments

Fig. 9. Refractive indices of various yellow pigments compared to aqueous and drying oil mediums.

The following is based on color effects in Artists Handbook of Materials and Techniques by Ralph Mayer (Mayer 1985).

Refraction of light

Refraction of light. A light ray passing through a sheet of glass or other transparent material bends (is refracted) and takes a shortcut. The angle of refraction varies with each substance and increases according to the power of each substance to impede light.

Transmission and reflection of light

Transmission and reflection of light. Under average conditions a certain amount of light is also reflected from the surface of clear glass as from a mirror. The proportions of light reflected and transmitted vary according to the nature of the substance, the surrounding conditions, and in many cases, the angle from which the surface is viewed.

Absorption of light

Absorption of light. Thin, translucent milk glass or other semi-opaque material transmits less light than does a transparent material. In this instance, some of the light is reflected, and some absorbed. The more the light is impeded and absorbed, the greater the opacity.

Dark surfaces

Dark surfaces. The greatest amount of light absorption, accompanied by the least reflection, occurs when light falls on a dead mat, intensely black surface. Other issues being equal, a brilliant white surface will reflect the most light, and as it is tinted the amount of reflection will decrease according to the depth of color.

White grounds

White grounds. When a layer of paint composed of pigment particles and binder is coated on a white ground the resulting reflection of light contributes brilliance and luminosity, which are altogether lacking when the painting is done on a black ground.

Colored and dark grounds

Colored and dark grounds. Any coloration of the ground will tend to decrease the amount of reflection, and the more translucent the coating is or becomes, the more the brightness of the resulting painting will be affected.


References

F. Donald Bloss, An Introduction to the Methods of Optical Mineralogy, New York: Holt, Rinehart and Winston, 1961, pp. 6, 131–142, 200–203.

Robert L. Feller, editor, Artists Pigments: A Handbook of Their History and Characteristics, Vol. I, New York: Oxford University Press, pp. 289–291.

Henry A. Gardner, George G. Sward, Paint Testing Manual, ASTM International, January 1, 1972, p. 79.

Rutherford J. Gettens and George L. Stout, Painting Materials: A Short Encyclopedia, New York: D. Van Nostrand Co., 1942, republished New York: Dover Publications, 1966, pp. 147–148.

Norris W. Jones and F. Donald Bloss, Laboratory Manual for Optical Mineralogy, Minneapolis, Minnesota: Burgess Publishing Co., 1980, pp. 3-1-3-5.

A. P. Laurie, The Painters Methods and Materials, New York: Dover Publications, 1988, pp. 102–110.

Ralph Mayer, The Artists Handbook of Materials and Techniques, 5th edition, New York: Viking Press, 1985, pp. 159–161.

H. E. Merwin, "Optical Properties and Theory of Color of Pigments and Paints," Proceedings of the American Society for Testing Materials, XVII (1917), pp. 494–530.

Alexander N. Winchell and Horace Winchell, Elements of Optical Mineralogy: An Introduction to Microscopic Petrography, Part II Description of Minerals, 4th edition, New York: Wiley and Sons, 1951.