light, colour & photography

reflection

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Light reflects to a greater or lesser extent at every surface. There is no surface that is truly black; none that will absorb all the incident light. A small proportion of light will always be reflected. The light that is reflected from objects makes them visible. But it is the light that is reflected from smooth surfaces that fascinates us most.

Figure 1: reflection of distant hills on the flat surface of a lake

Figure 2: reflections at the surface of a shiny sphere

It is only through reflections that we first catch a glimpse of how we ourselves appear. This short article aims to cover familiar territory: the way light reflects from surfaces and how light is refracted at the boundary of a transparent medium.

specular reflection

We are most aware of reflections from shiny objects. This is known as specular or mirror-like reflection. It is the sort of reflection observed on polished metal surfaces and on the surface of liquids. Sunlight reflecting off water is a very common type of specular reflection. The essential thing is that the image is in some way preserved as shown in the photograph in Figure 1. Even in a non-plane surface such as a sphere a geometric transformation of the image takes place but the image is nonetheless present as shown in Figure 2.

The simplest geometry is for a reflection at a plane (optically flat 1 2) surface. Such a surface will appear mirror-like irrespective of the material from which it is made. Figure 3 shows the arrangement with an incident beam of light to the left and the reflected beam to the right. A perpendicular line drawn at the point of reflection on the surface is called a normal.

Figure 3: specular reflection at a plane surface

As long ago as the first century BC 3 it was known that the angles between the two incident beams and the normal are equal 4. This is expressed as θ_i = θ_r where θ_i is the angle of incidence and θ_r is the angle of reflection. Although this is taught in schools as the Theory of Reflection, the term specular is seldom referred to.

diffuse reflection

The general line of thought is that smooth flat surfaces give rise to specular reflections; rough surfaces give rise to diffuse reflections. But this is not the case. What we have said about specular reflections isn't quite true. If light were to be reflected solely according to the Law of Reflection, the surface could not be seen at any angle other than the angle of reflection. Real world objects viewed at a macro level don't just disappear as if into a black hole just because we change the angle at which we look at them. This is because diffuse reflection always occurs even if it is to a minimal amount. To illustrate this we can take the example of three different materials: polished aluminium, polished black granite and polished sichuan marble.

polished aluminium

Often used for so-called front-silvered mirrors. Characterised by very high reflectivity, metallic lustre, high specular reflection, low diffuse reflection. It is axiomatic to state that such a surface has a mirror-like appearance. Because the aluminium is chromatically neutral we tend not to notice the surface itself but only the objects reflected in it.

polished black granite

Most "black granite" sold for work surfaces and counter tops is probably a basalt because of the lack of quartz and feldspars. Characterised by low reflectivity, non-metallic lustre, low specular reflection, low diffuse reflection. We can see reflections of world objects in the surface of polished black granite but the reflections lack brightness because of the high absorbtion of light at the surface and the consequent lack of diffuse reflections. Whatever way we look at such a surface it always appears black.

polished sichuan marble

A very white marble highly prized for making statues and busts. Characterised by high reflectivity, non-metallic lustre, low specular reflection, high diffuse reflection. The surface smoothness of the marble can equal that of polished black granite and its reflectivity can approach that of polished aluminium or coated papers. Yet, for all that it is polished, it will still look white and never gain anything of a metallic lustre. The extent to which diffuse reflection exceeeds specular reflection means that it is almost impossible to discern the reflection of world objects in the surface.

There are three important distinctions arising from these comparisons:

1. with a diffuse reflection the image is never preserved
2. surface polish and smoothness has little to do with the balance between specular and diffuse reflections
3. a material's reflectivity determines whether its surface appears white or black or somewhere inbetween

Walk past a row of cars and you will notice that the shiniest cars are always black. Although a white car appears brightest it is in the black car that you notice the reflections of the objects that surround it. It is these specular reflections that give to polished black its shiny appearance. The problem with a polished white car is that the random diffuse reflections mask any specular reflections.

Figure 4 gives an impression of diffuse and specular reflection at a plane surface where the specular component dominates. Figure 5 gives an impression of diffuse reflection at a non-plane surface where diffuse reflection dominates.

A perfectly diffuse reflector is known as a Lambertian reflector.

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