1.2. Reflection and refraction

In order to form images, telescopes use mirrors and lenses. Mirrors are optical surfaces that reflect light. And lenses are optical elements that refract light. Both, reflection and refraction of light result from its wave nature.

Reflection occurs when a surface exposed to light immediately emits back a portion of the energy received. As the surface atoms absorb wave energy, they become unstable, and regain stability by releasing portion of the absorbed light from their electron orbits. Due to reflection of light occurring in a precisely consistent, predictable manner, reflective surfaces can be manipulated to re-direct or re-shape optical wavefront into spherical, needed for the purpose of imaging. This can be illustrated with a linear array of three silver atoms on the mirror surface (FIG. 3). With the atoms being separated by ~1 Ångström (one 10-millionth of mm), the array is essentially flat. As the incident wavefront sweeps over the array, the atoms absorb wave energy and emit most of it right back. However, if the array is inclined in regard to the incident wavefront, the surface slope causes phase shift, with each successive atom's emission lagging behind by a fixed phase fraction. This in turn results in the change of orientation of the principal wavefront, so that the angle of reflection is a negative equivalent of the angle of incidence. In other words, the wavefront reflects at the angle of incidence, only at the opposite side of the normal to the surface.

FIGURE 3: Reflection of light waves: flat incident wavefront section Wi, oriented vertically, strikes reflecting surface S inclined at an angle α, exciting its surface atoms. The atoms absorb and re-emit wave energy in all directions. Due to the wave emission from each next atom being delayed in time, it is also delayed by the phase fraction δ. It causes the orientation of line of points in phase change from pp1 to p'p1', as determined by the pp1p1' and pp'p1' triangle identity. As a result, reflected wavefront section Wr forms directed at an angle α'= -α to the surface normal, and at an angle 2α to the incident wavefront section. The minus sign indicates that this new direction forms on the opposite side of the surface normal (plane of reflection at any surface point is determined by the impinging ray and the normal). This is the law of reflection of light. The form of reflected wavefront is determined by those of the incident wavefront and the surface. Proper combination of the two will produce spherical reflected wavefront. Waves emitted by atoms to directions other than that indicated by the law of reflection do not form effective wavefronts, due to the phase difference being increasing with the deviation from direction of the principal wavefront, as illustrated in Fig.1.

Rays from the neighboring atoms are practically parallel, but they will merge and interfere in the focal zone of the mirror. As the mirror slope gradually changes along its surface, so does the slope of reflected wavefront unfolding from the mirror edge toward center. If the mirror surface has appropriate shape, the reflected wavefront will emerge spherical, with the tightest possible concentration of light energy forming around its center of curvature.

Refraction of light also results from the phase shift of wavefront points, as their velocity changes within media of different optical properties. The ratio of velocity change is expressed by refractive index n as 1/n. Value of n spans from 1 for vacuum, to nearly 1.8 for the most dense commonly used optical glass types. An average refractive index of the optical crown is n~1.5, reducing the speed of light by a factor ~1/1.5. Refractive index for any given media vary slightly with the wavelength of light, resulting in unequal propagation for different wavelengths - the cause of chromatic aberration.

An exaggerated section of a lens can be used to illustrate the phenomenon, mathematically described by Snell's low of refraction (FIG. 4). The lens surface is practically flat for a very small section, and inclined in regard to impinging wavefront at a local surface slope angle. As incident wavefront enters the glass, it slows down, while its portions still traveling through the air maintain the higher speed. This generates phase shift resulting in the change of wavefront orientation. With properly designed lens objective, these sections of refracted incident wavefront unfold into a sphere. Of course, for proper refraction, the glass has to be homogeneous, just as any other media through which light travels.

FIGURE 4: Section of a wavefront as it travels through media of different refractive indici. The increase in phase shift δ caused by combination of surface slope and slower in-glass speed of light changes the orientation of the incoming wavefront section W into that of the refracted section W', according to the law of refraction (also: Snell's law): sines of the refracted angle α' and incident angle α - measured from the normal to the surface - relate as the incidence index n to the index of refraction n', thus sinα'/sinα=n/n', or nsinα=n'sinα'. Wavefront orientation changes again into W'' as it re-enters medium of lower refractive index. Phase shift δ' results in the incidence angle β to change into refracted angle β'. Small angles (in radians) nearly equal their sines, which simplifies the law to α'/α=n/n'. Setting n'=-n results in α'=-α, the law of reflection.

Local variations in glass density would cause local deformations of the wavefront, resulting in wavefront roughness.

◄ 1.1. Diffraction in a telescope ▐ 1.3. Optical system of a telescope ►

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