Optical properties of materials are char- acterized in part by their refraction of light. Light incident at the interface be- tween two materials has a transmitted component whose direction changes as it passes the interface. For example, rays of light change direction, or are “refracted,” when passing from air into glass. As shown in Figure 6.5, one component of light is reflected, while the other compo- nent is refracted. The refracted beam changes direction at the interface and de- viates from a straight continuation of the incident light ray. A similar effect can be seen in the apparent bend in a straight stirring rod immersed in a liquid. In Fig- ure 6.6a the beaker is filled with air, and hence the entire length of the rod is in the same medium, air, and appears straight.
The beaker in Figure 6.6b is partially filled with water. The stirring rod therefore passes through two media, air and water. At the air/water in- terface the rod appears to bend.
The change in direction of light as it passes from one medium to an- other is associated with a change in velocity. When visible light in air en-
6.2 Refraction
69
Fig. 6.6a,b. Photographs of a stirring rod in a beaker. Photograph (a) is of an empty beaker, and the glass rod appears straight. Photograph (b) is of a beaker partially filled with water. The rod appears to be bent at the water surface.
Fig. 6.5. Light in air incident on a glass surface where it is partly reflected at the interface and partly transmitted into the glass. The direction of the trans- mitted ray is changed at the air/glass surface. The angle of refraction ris less than the angle of inci- dence i.
ters a medium such as glass, the velocity of light decreases to 75% of its velocity in air, and in other materials the decrease can be even more sub- stantial. For example, in binders such as linseed oil, the velocity decreases to 66% of its velocity in air. Figure 6.7 displays in bar chart format the velocity of light in different media. The 100% value is the velocity of light in a vacuum. For air, the velocity is 99.7% of the speed in a vacuum. For some pigments such as titanium (Ti) white, the velocity decreases to 40%. Refraction is an effect that occurs when a light wave passes a bound- ary from one medium into another in which there is a change in veloc-
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Fig. 6.7. Bar chart of the velocity of visible light in different media. The value of 100% refers to the velocity of light in a vacuum.
Fig. 6.8. Light waves of wavelength lincident on glass change direction and wave- length when transmitted into the glass.
6.2 Refraction
71
ity of the light. Light is therefore refracted when it crosses the interface from air into glass, in which it moves more slowly. We illustrate refrac- tion in Figure 6.8 by representing incident light as parallel waves with a uniform wavelength, lambda, . As the light enters the glass the wave- length changes to a smaller value, lambda prime, . Wave a passes the air/glass interface and slows down before wave b, c, or d arrives at the interface. The break in the wave front intersecting the interface occurs when waves aand b have entered the glass, slowed down, and changed direction. At the next wave front in the glass, all four waves are now trav- eling with the same velocity and wavelength .
The waves are continuous and remain connected as they pass from one medium to another. The wave inside the new medium is moving more slowly. For waves traveling at an angle to the surface, this slower velocity causes the waves to change direction. The greater the change in velocity, the greater the change in direction. Figure 6.9 shows the change in direction for light in air incident at 45° both on water with refracted angle of 32° and on Ti white with a refracted an-
gle of 16°. These angles correspond to the differ- ences in velocity shown in Figure 6.7.
The ratio of the velocity of light in a vacuum to the velocity of light in a medium is referred to as the medium’s refractive index. Refractive in- dices are most easily determined from the mea- sured values of the incident angle and the angle of refraction and their geometric relationship de- scribed in Appendix B. Values of the refractive in- dices for the media shown in Figure 6.7 are given in Table 6.1. A more comprehensive list of values
Fig. 6.9. Light incident at 45° on water and Ti white. The angles of refraction (32° for water, 16° for Ti white) are determined by the refractive indices, which are 1.33 for water and 2.5 for Ti white. The reflected components are not shown.
Values of Refractive index
Medium Refractive Index
Air 1.003 Water 1.33 Linseed Oil 1.48 Cobalt Green 2.0 Titanium White 2.5 TABLE 6.1
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of the refractive index is given in Ap- pendix B, Table B.1.
Refractive indices correlate to the perceived relative transparency or opac- ity of a medium. The media above, com- monly found in paintings, range from water (a diluent in many paints) with a refractive index of 1.33 and very trans- parent to titanium white with a refrac- tive index of 2.5 (a very opaque white pigment).
The path of light in air incident on and transmitted through a glass plate is shown in Figure 6.10. The angle of the incident ray to the normal is 45° and equals that of the reflected ray. The transmitted ray is refracted at an angle of 28° to the normal and exits the glass at an angle of 45° to the normal, an an- gle equal to that of the incident ray. This explains why, for example, the image we see through a flat-glass window pane is virtually unchanged from that seen through an open window.
6.3
SCATTERING OF
LIGHT
The transparency or opacity of a paint layer depends on the amount of scattering and absorption of the light. Scattering in paint films is the deflection of light rays by pigment particles suspended in a binding medium. Scattering depends on the difference in index of refraction be- tween the paint pigment particle and the surrounding binding medium. If the difference in the refractive indices of the pigment particle and the binding medium is large, then the pigment deflects light effectively. For example, a particle of titanium oxide white pigment with a refrac- tive index of 2.5 suspended in a medium of linseed oil with a refractive index of 1.5 will scatter light very effectively. A particle of ultramarine blue pigment with refractive index of 1.5 suspended in the same linseed oil medium will appear transparent because the refractive indices are closer on both sides of the interface, and little scattering will take place. Painters utilize the differences in opacity and transparency resulting from these relationships in organizing many aspects of their paintings, including the mixing of colors and the sensation of luminosity in the paint films.
Fig. 6.10. Light incident on a glass plate. The re- flected part of the ray is shown along with the light path for the refracted component.
6.4 Absorption of Light
73
The size of the pigment particle also influences the amount of scat- tering. Particles of about the same size as the wavelengths of visible light are more effective in scattering visible light than particles much larger or smaller. For example, centimeter size titanium oxide crystals are trans- parent, but when ground down to about 500 nanometers they scatter vis- ible light very strongly. The amount of scattering also depends on the density of particles (number per unit volume) in the medium. The higher the density, the greater the amount of scattering. White correction fluid is a dense aggregation of titanium oxide particles suspended in a liquid medium. The opacity of the correction fluid is determined by the den- sity as well as the difference in refractive index and the particle size.
6.4
ABSORPTION OF
LIGHT
As we pointed out in Chapter 5, the mechanism for the production of color by materials is the selective removal of certain wavelengths (or en- ergies) of light from the electromagnetic spectrum. The light penetrates into the material and encounters light-absorbing pigment particles for this selective removal to occur. A photon transfers all of its energy to the absorbing pigment and is “lost,” absorbed, that is, from the light beam. The nonabsorbed photons are scattered (or reflected) back from the pig- ment particle, producing the sensation of color specific to the pigment. The absorption of light is illustrated by a beam of light of given in- tensity (or flux of photons) that penetrates into a material containing a given density of pigment particles that absorb or transmit the photons. The photons penetrate into the material and are
absorbed at different depths (Figure 6.11). We also show in Figure 6.11 that some pigments (shaded) will not absorb certain photons. For example, red pigment particles will not absorb photons of light with wavelengths of around 700 nm, but will absorb photons of light with wavelengths of 400– 500 nm (blue).
The amount of light that is absorbed is not de- pendent on the intensity of the incident light, but is determined by the density of pigment particles. If the concentration of pigment particles is in- creased, the amount of absorption is increased and the amount of transmitted light is decreased. The intensity of light passing through a layer of paint will decrease with depth.
Paints with high concentrations of pigment and relatively small amounts of binder (casein, for
Fig. 6.11. Flux of photons incident on a transparent medium containing pigment particles, which either absorb the photons (unshaded particles) or transmit the pho- tons (shaded particles).
example) rely mostly on surface absorption of light to produce color. The color of these paints changes dramatically when they are covered with varnish (Color Plate 21). The simplest change in appearance is the change from a rough matte surface (diffuse reflection when light is scattered in all directions from an irregular surface) to a smooth, glossy surface (spec- ular reflection, where light is reflected in one direction). The varnished paint surface is glossy, and more light is reflected from the varnish sur- face than from the uncovered paint, leaving less light to be transmitted to and absorbed by the paint layer. This is the source of the darkening effect of a varnished surface. Darkening results from the lower light in- tensity incident on the paint layer under the varnish.
When the varnish layer is applied, we change the index of refraction relations as shown in Figure 6.12. The reflection of light at the paint layer under a coat of varnish is less than that for the unvarnished paint layer because the difference in refractive indices is smaller at the paint–varnish interface than at the paint–air interface. Once inside the varnish layer, a greater percentage of the light is transmitted into the paint. As a result, more light can be absorbed by the pigment particles, and this will lead to a deeper and richer color.
This concept is applied by painters through the use of a glaze,which is a colored, translucent layer of paint applied over another layer of color. The underlying color is typically opaque, although multiple layers of glaze are sometimes used. The light reflected from the opaque under- layer is filtered by the translucent glaze, resulting in a desired change in color. The colors produced by glazing techniques follow the subtractive color relationships (described in Chapter 5) arising from the absorption and scattering of light by pigment particles in the glaze. Glazes, like var- nishes, darken the underlying color slightly and increase the reflective properties of the paint film.
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Fig. 6.12a,b. Cross section of paint film (a) without and (b) with varnish layers. The values of the refractive indices are given in parentheses.