2Optics
Light
Physiological optics treats topics that are relevant for understanding how images are formed in the eye. Geometric optics treats light as bundles of straight lines or beams, like when the light from a pinhole passes through a smoke cloud or, in a laboratory demonstration, through a bowl of glass filled with a blend of water and skimmed milk. It was Euclid (about 300 BC) who introduced the concept of light rays (Grini, 1997). In modern physics light is described dualistically as a wave and as a stream of particles. The concept of the wave nature of light is attributed to Christiaan Huygens (1629–1695). Isaac Newton (1642–1727) preferred the particle theory, and these two theories were considered to be in conflict with each other. Even today we do not have good unifying alternatives to the dualistic concept, and this is a dilemma to anyone who wishes to ‘explain’ light. Modern theories combine the wave concept and the concept of photons, and we use either the particle or the wave analogy depending on which one best suits the phenomenon being dealt with.
Figure 2.1 shows light as a part of the spectrum of electromagnetic radiation. Light – or visible radiation – is the small ‘window’ in this spectrum that allows us to see with our eyes, as a small part of a much greater spectrum that consists of everything from radioactive radiation to radio waves. Normal eyes can detect radiation with wavelengths, , between 380 (violet) and 760 nm (red).
1 nanometer ¼ 1 nm ¼ 0:000000001 m ¼ 10 9 m
For wavelengths below 380 nm, and down to about 100 nm, the radiation is called ultraviolet light (UV ), although this radiation does not lead to a visual impression, which is normally associated with light. Above 780 nm and up to a wavelength of 1 mm (1 000 000 nm), the radiation is called infrared light (IR).
Light Vision Color. Arne Valberg
# 2005 John Wiley & Sons Ltd
36 |
OPTICS |
Figure 2.1 The visible range of the electromagnetic spectrum stretches from 380 to 760 nm. In addition to visible light, the electromagnetic spectrum consists of shorter-wavelength ultraviolet radiation, radioactive X-rays and longer-wavelength, infrared radiation, microwaves and TV and radio waves. See also Color Plate Section.
The description of light as a stream of particles, called quanta or photons, goes back to the beginning of the twentieth century. Quanta are small ‘energy-packets’, each with an energy, E, that is proportional to the light’s frequency, :
E ¼ h
h is a universal constant, called Planck’s constant, and the frequency, , represents the number of cycles of oscillation the wave completes per second. This equation can also be written as
E ¼ hc=
where c is the speed of light. As for any wave, the speed of light is a product of its wavelength and frequency, c ¼ . Albert Einstein’s (1879–1955) theory of relativity was developed on the assumption that the speed of light in vacuum is a universal constant.
The higher the frequency of electromagnetic radiation (and the shorter the wavelength), the more energy there is in each quantum. Radioactive -radiation and X-rays have higher quantum energy than visible light. TV and radio stations broadcast at frequencies where the wavelengths range from 1 m to 30 km. The quantum energy for this radiation and also for microwaves is lower than that of visible light. In vision, the particle nature of light is of practical importance only at very low intensities, close to the absolute threshold for night vision.
Regardless of wavelength, light and all other electromagnetic radiation propagate with a speed c ¼ 299 792 458 m=s in vacuum (or about 300 000 km=s ¼ 0:3 m=ns;
LIGHT |
37 |
1 ns ¼ 10 9 s). In an optically more dense material the speed of light will be lower. Since the speed of light in vacuum is constant, the length of a standard meter is now defined as the distance that light travels in vacuum in a time interval of 1/299 792 458 of a second. The meter-stick, which was previously used as a length standard, and which is kept in Paris, is therefore now obsolete.
Ultraviolet radiation
Most of the sun’s ultraviolet radiation (UV) below 380 nm is absorbed by the ozone layer in the Earth’s atmosphere. The long-wavelength ultraviolet radiation closest to visible light (from 315 to 400 nm) has been given the name UV-A. The next, somewhat more energy-rich region of the spectrum, is called UV-B (280–315 nm), while the highest-energy ultraviolet region (100–280 nm) is referred to as UV-C. While the cornea of the eye is transparent for both UV-A and UV-B, all ultraviolet light (UV-A, -B, -C) is absorbed by glass. Ultraviolet radiation can cause absorption of light in a substance and excitation of electrons from lower energies to higher energy levels in atoms and molecules. When returning to lower energies, longerwavelength visible light is emitted, a process called fluorescence. Materials such as teeth, bones and minerals fluoresce on exposure to UV, as do some optical whiteners used with paper and textiles.
With respect to its effect on humans, ultraviolet light has ‘two faces’; a positive effect initiating the synthesis of vitamin D, which is important for calcium to be absorbed in bone and tissue, and the harmful effect of provoking skin cancer and cataract. Sunburns (of the skin) and inflammation of the cornea are also well known effects of exposure to intense sunlight. UV-C kills germs and bacteria and is therefore often used to sterilize instruments.
Infrared radiation
Infrared radiation (IR) is heat radiation with wavelengths longer than 780 nm. About half of the energy of the sun reaching the surface of the earth is in the visible spectrum range, and only about 3 percent of the total is in the ultraviolet. The rest is life-giving infrared radiation.
Infrared cameras register temperature differences, and can be used to ‘see’ in the dark. They can also be used to see through opaque films. In a painting, for instance, infrared radiation is less effectively scattered by small particles in varnish films than visible light, and it is able to overcome the opacity of the upper layers of the painting. It therefore becomes possible to observe detail in the paint layer which has become obscured by old varnish. Forgeries can sometimes be detected in this way.
Infrared radiation is absorbed by water and by all the media in front of the retina. Only a small percentage of IR radiation reaches the retina. Overexposure to infrared
38 OPTICS
radiation may cause cataract, as indicated by the expression ‘a glassblower’s cataract’.
Light sources
Light and its effect on the organ of vision is the subject of all chapters in this book. Here, we want to introduce some fundamental physical concepts that will be used later. Let us start with the black body radiator. A black body thermal radiator emits light with intensity and spectral distribution depending on the temperature of the material (usually a metal). A tungsten filament lamp comes close to being such a light source. The higher the temperature is, the shorter the wavelength of maximum energy. At low temperatures, most of the energy is in the infrared region. Even around room temperature, the black body radiates energy. Visible light begins to appear around 1000 K (1 K ¼ 273 C), and ultraviolet does not appear before the temperature has reached about 2000 K. At about 3000 K, the source looks bright yellow, and at 5000 K, approximately the temperature of the sun’s surface, energy is about evenly distributed over the visible spectrum, and the body appears white. At still higher temperatures, the radiating body becomes bluish.
The color of natural and artificial illumination can be compared with that of a black radiating body radiator of a certain temperature. The temperature of the body that gives the closest color match is called the correlated color temperature of the light source. This characterizes the color of a wide range of illuminants, including fluorescent light, although the actual temperature of the fluorescent light may be rather different from that of the black body radiator (it depends more on the source’s spectral distribution). The color of different daylight phases also comes close to that of a black body radiator of different temperatures. Color temperature is more meaningful when comparing sources having about the same spectral distribution. Incandescent light has a spectral distribution that comes close to that of the black body. The color temperature of the light from a common tungsten filament is in the range 2700–3200 K, depending somewhat on wattage. However, such lamps are not very efficient light sources. Most of the energy is released as heat, and only about 15 percent is released as light. Color rendering is a problem. Because the light is yellowish, it is difficult to see yellow lines on a white paper, and it is also hard to distinguish slightly different blue shades.
Fluorescent lamps are gas-filled tubes with a material coating, called phosphor, on the inside of the tube. When the ultraviolet radiation emitted by the mercury gas excites the phosphor, it fluoresces and radiates visible light. The result is a broad spectral distribution of emitted light with superimposed emission lines from the mercury gas.
Light from all kinds of light sources affects the color appearance of surfaces, for instance a blue surface looks different in daylight and in incandescent light, but it is usually hard to predict such differences (see chapter on Color rendering, p. 268).