Part I
Light, Sight and Colour
1
Light
L. C. Wiltshire
The subject of this book is the modern technology involved in the production and utilization of light. Much of our information about the external world is gained through the visual sense and therefore adequate lighting is of major importance in everyday life. This first chapter begins with a short survey of some of the physical aspects of light and with statements of fundamental laws governing its behaviour. Next there is a section on the manner in which the eye responds to stimulation by light, and this is followed by definitions of quantitative measures used for calculations in the lighting field.
1.1 Electromagnetic Radiation and Light
Light is a form of energy that can pass from one material body to another without the need for any material substance in the intervening space. Such energy transfer has come to be called radiation, a term which implies that the energy flows out in straight lines in all directions from the source, although in fact straight-line flow does not always occur, particularly when material substance is traversed. Some forms of radiation are known to consist of particles, for example those which are emitted by radioactive materials, and light was at one time thought to consist of a shower of particles, but later it was found by experiment that the behaviour of a light ray could be better described in terms of waves, the ray direction being the direction in which the waves are travelling. About 100 years ago it became clear that light waves are electromagnetic in character and occupy only a very small part of a huge range of wavelengths that constitute the electromagnetic spectrum (Figure 1.1). At the long-wave end of this spectrum there are electromagnetic waves used for radio communication, with wavelengths ranging from tens of kilometres down to a few millimetres. At the other end of the electromagnetic spectrum there are X-rays and gamma rays, the latter being emitted during nuclear reactions and having wavelengths which are small even compared with atomic dimensions.
Fig. 1.1 The electromagnetic spectrum.
1.1.1 The Visible Spectrum
The visible portion of the spectrum covers the wavelength range from approximately 380 nm to 780 nm (1 nm=10â6 mm) and the eye discriminates between different wavelengths in this range by the sensation of colour. Blue and violet correspond to the short wavelengths and red to the long, yellow and green being in the middle of the visible range of wavelengths. Light consisting of a single wavelength radiation is said to be monochromatic, and is not strictly obtainable in practice because all sources produce light covering at least a narrow band of wavelengths. The laser comes the closest to being a perfectly monochromatic light source.
Radiation reaching the earthâs surface from the sun covers a range of wavelengths from about 290 nm to 1700 nm, which is considerably broader than the visible spectrum. At wavelengths shorter than 290 nm, solar radiation is absorbed by ozone in the upper levels of the earthâs atmosphere, and in the region beyond 1700 nm there are strong absorptions due to water vapour and carbon dioxide in the lower atmosphere (Henderson 1977).
1.1.2 Ultraviolet and Infrared Radiation
Electromagnetic radiations with wavelengths just beyond the violet and red ends of the visible spectrum are known, respectively, as ultraviolet and infrared radiations. The ultraviolet is considered to extend down to a wavelength of 1 nm, below which the waves are regarded as X-rays, and the infrared extends up to an arbitrary wavelength limit of 1 mm, at which point the radio region begins. While not perceptible to the eye, both ultraviolet and infrared radiation can be detected physiologically, if sufficiently intense, as a sensation of heat on the skin. This emphasizes the fact that all radiation can degenerate to heat when absorbed, and also that there is no special heating effect associated with infrared radiation, as is commonly supposed. In addition, ultraviolet radiation with wavelengths less than 320 nm can cause damage to living tissues, manifested on the skin as a delayed erythema (reddening) and blistering (section 1.4.3).
1.2 Propagation of Light
Light and all other electromagnetic radiations travel through a vacuum in straight lines at the same velocity, which is close to 300 000 km sâ1. In a material medium, such as air or glass, the velocity of propagation is less than in a vacuum by a factor known as the refractive index of the medium.
For any type of wave the velocity v is equal to the product of the wavelength Ν and the frequency ν
where frequency is defined as the number of waves which pass a fixed point in one second. For example the waves of violet light with a wavelength of 400 nm in vacuum have a frequency of 7.5 Ă 1014 Hz, and red light of 750 nm wavelength has a frequency of 4 Ă 1014 Hz. When waves pass from one medium to another the frequency does not change, but any change in velocity is accompanied by a proportional change in wavelength since by equation (1.1) v/Îť must be constant. When the wavelength of light is quoted without reference to a medium it is normally taken to be the wavelength in air, which will be only very slightly shorter than that in a vacuum since the refractive index of air is close to unity.
At the boundary between two media having different refractive indices, incident light waves split into two groups â one is reflected back into the first medium and the other group is refracted into the second medium, as shown by the ray diagram in Figure 1.2. The directions of the reflected and refracted rays are governed by the laws of geometrical optics, which can be derived from the wave theory of light and are stated in the following two subsections.
Fig. 1.2 Reflection and refraction at a boundary between two media.
1.2.1 Laws of Specular Reflection
At a bounding surface that is smooth compared with the wavelength of the incident light, specular reflection is said to occur. A single incident ray produces a single reflected ray and the following relations hold:
⢠The incident ray, the reflected ray and the perpendicular to the bounding surface at the point of incidence all lie in one plane.
⢠The incident ray and the reflected ray make equal angles with the perpendicular and are on opposite sides of it.
The proportion of light energy which appears in the reflected ray depends, among other things, on the ratio of the refractive indices of the two media and on the angle of incidence, that is the angle between the incident ray and the perpendicular to the surface. As the angle of incidence approaches 90° the proportion of reflected light approaches 100 per cent.
1.2.2 Laws of Refraction
Light passing through a smooth boundary surface into the second medium suffers a change of direction according to the following laws:
⢠The incident ray, the refracted ray and the perpendicular to the surface at the point of incidence all lie in one plane.
⢠If the incident ray is in a medium of refractive index n1 and makes an angle θ1 with the perpendicular to the surface, and the refracted ray is in a medium of refractive index n2 and makes an angle θ2 with the perpendicular, then
where θ1 and θ2 lie on opposite sides of the perpendicular (Snellâs law).
The above laws of refraction apply to most common materials, such as glass, transparent plastics and liquids. In the case of certain crystals and transparent solids which are under strain these laws do not apply exactly, but the complicated effects which are observed under these conditions will not be discussed here.
1.2.3 Total Reflection
When a ray passes from a high to a low refractive index medium, such as from glass to air, a refracted ray exists only if θ1 is less than the critical angle, which is equal to sinâ1 (n2/n1). The critical angle corresponds to θ2 = 90° in equation (1.2), and for glass of refractive index 1.5 has the value 41° 49â˛. If a ray is incident at an angle greater than the critical angle, no refracted ray is present and all of the incident light energy appears in the reflected ray; hence the term âtotal reflectionâ is used for this condition. Total reflection provides a means of obtaining an efficient specular reflector and finds use in prismatic binoculars, reflective signs and luminaires (Bean and Simons 1968). Another application is known as fibre-optics where light is channelled along transparent rods or fibres, which can be curved if required.
1.2.4 Dispersion
Refractive indices are dependent on the frequency of the light waves, an effect known as dispersion, and for common materials the refractive index increases as the frequency increases. For sp...