Optics

I

Introduction

Optics, branch of physical science dealing with the propagation and behaviour of light. In a general sense, light is that part of the spectrum of electromagnetic radiation that extends from X-rays to microwaves and includes the radiant energy that produces the sensation of vision. The study of optics is divided into geometrical optics and physical optics, and these branches are discussed below.

II

Nature of Light

Radiant energy has a dual nature and obeys laws that may be explained either in terms of a stream of particles, or packets of energy, called photons, or in terms of a train of transverse waves (see Wave Motion). The concept of photons is used to explain the interactions of light and matter that result in a change in the form of energy, as in the case of the photoelectric effect or luminescence. The concept of waves is usually used to explain the propagation of light and some of the phenomena of image formation. In light waves as in other types of electromagnetic wave, there are rapidly fluctuating electric and magnetic fields at each point in space. Since they have both direction and magnitude, the fields are vector quantities. The electric and magnetic fields are at right angles to each other and to the direction of movement of the wave. The simplest sort of light wave is a pure sine wave, so called because a graph of the electric or magnetic field intensity drawn along the direction of travel at any moment would trace out a sine curve. The number of complete oscillations, or vibrations, per second of a point on the light wave is known as the frequency. The wavelength is the distance parallel to the axis between two points of the same phase—that is, points occupying equivalent positions on the wave. For example, the wavelength equals the distance from maximum to maximum or from minimum to minimum of the sine wave. In the visible spectrum differences in wavelength manifest themselves as differences in colour. The visible range extends from about 350 nanometres (violet) to 750 nanometres (red), a nanometre being equal to a billionth of a metre, or 4 × 10^-8 in. White light is a mixture of the visible wavelengths. No sharp boundaries exist between wavelength regions, but 10 nanometres may be taken as the low-wavelength limit for ultraviolet radiation. Infrared radiation, which includes radiant heat energy, spans the wavelengths from about 700 nanometres to approximately 1 millimetre. The speed of an electromagnetic wave is the product of the frequency and the wavelength. In a vacuum this speed is the same for all wavelengths. The speed of light in material substances is less than in a vacuum, and is different for different wavelengths, an effect called dispersion. The ratio of the speed of light in vacuum to the speed of a particular wavelength of light in a substance is known as the index of refraction of that substance for the given wavelength. The index of refraction of air for all wavelengths is 1.00029, but for most applications it is sufficiently accurate to take it to be 1.

The laws of reflection and refraction of light are usually derived using the wave theory of light introduced by the 17th-century Dutch mathematician, astronomer, and physical scientist Christiaan Huygens. Huygens’ principle states that every point on an initial wave front may be considered as the source of small, secondary spherical wavelets that spread out in all directions from their centres with the same speed, frequency, and wavelength as the parent wave front. A new wave front can be defined, encompassing the wavelets. Since the light progresses at right angles to this wave front, changes in the direction of the light can be worked out using Huygens’ principle.

When the wavelets encounter another medium or object, each point on the boundary becomes a source of two new sets of waves. The reflected set travels back into the first medium, and the refracted set enters the second medium. The behaviour of the reflected and refracted rays can be explained by Huygens’ principle. It is simpler and sometimes sufficient to represent the propagation of light by rays rather than by waves. The ray is the flow line, or direction of travel, of radiant energy. In geometrical optics the wave theory of light is ignored and the assumption is made that light does not bend round corners. This approximation is valid when lenses, apertures, and so on are large in comparison with the wavelength of the light. Rays are traced through an optical system by applying the laws of reflection and refraction.

III

Geometrical Optics

This area of optical science concerns the application of laws of reflection and refraction of light in the design of lenses (see Lenses below) and other optical components of instruments.

A

Reflection and Refraction

If a light ray that is travelling through a homogeneous medium is incident on the surface of a second homogeneous medium, part of the light is reflected and part may enter the second medium as the refracted ray, and may or may not undergo absorption there. The amount of light reflected depends on the ratio of the refractive indexes for the two media. The plane of incidence is defined as the plane containing the incident ray and the normal (that is, the line perpendicular to the surface) at the point of incidence. The angle of incidence is the angle between the incident ray and this normal. The angles of reflection and refraction are defined correspondingly. The laws of reflection state that the angle of incidence is equal to the angle of reflection and that the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane. If the surface of the second medium is smooth it may act as a mirror and produce a reflected image. A light ray from an object striking a flat, or plane, mirror will be reflected away from the surface. To an observer in front of the mirror, the reflected ray appears to have come from a point behind the mirror that is a continuation of that reflected ray. The image of the object appears to lie as far behind the mirror as the object lies in front of it.

If the surface of the second medium is rough, then normals to various points of the surface lie in random directions. In that case, rays that may lie in the same plane when they emerge from a point source nevertheless lie in random planes of incidence, and therefore of reflection, so are scattered and cannot form an image.