# An Elementary Treatise on Optics/Introduction

INTRODUCTORY OBSERVATIONS.
1.Concerning the nature of light, very little is known with any certainty; fortunately it is not at all necessary in mathematical enquiries about it, to establish any thing about its constitution. The science of Optics reposes on three Laws, as they are technically termed, which depend for their proof upon Observation and Induction.
2.In the first place, as it is observed that an object cannot be discerned if it be placed directly behind another not transparent, we conclude that the action of light takes place in straight lines. These straight lines are called rays, and are the sole object of discussion in the following Treatise.
3.When a small beam of light admitted through a hole in the shutter into a dark room falls upon a plane polished surface, such as that of a common mirror, it is observed to be suddenly bent back, or reflected, according to the technical phrase, and as it has otherwise the same appearance as before, we conclude that each ray of light is bent at the point where it meets the surface, or that more properly for each ray that existed in the beam, we have now two, an incident and a reflected ray meeting in the surface.
Observation leads us to conclude that these rays are invariably in the same plane, and that they as invariably make equal angles with the reflecting surface, or with a line perpendicular to it at the point of reflection: the angles which the incident and reflected rays respectively make with this perpendicular are called the angles of incidence and reflection.
4.If again we present to the beam of light above-mentioned a very thick plate of glass or a vessel of water, or any other transparent substance, we shall find that part of the light is reflected on ​reaching the surface, but part enters the glass or water, not however without deviating from its former direction. It is in fact bent or refracted, so as to be more nearly perpendicular to the surface, so that the angle between an incident ray and a perpendicular to the surface, called as before, the angle of Incidence, is greater than that between the refracted ray and the perpendicular; this latter angle is technically termed the angle of Refraction.
Observations similar to those alluded to in the former case lead us to the conclusion that the angles of incidence and refraction are always in the same plane, and that though they do not bear an invariable ratio to one another, their sines do, provided the observations are confined to one medium, or transparent substance.
5.We have then these three laws upon which to found our theory.
   * The rays of light are straight lines.
   * The angles of incidence and reflexion are in the same plane and equal.
   * The angles of incidence and refraction are in the same plane, and their sines bear an invariable ratio to one another for the same medium.
Note. Sir I. Newton attempted to explain the Theory of Optics on the hypothesis that light is a material substance emitted from luminous bodies, and that the minute particles of this matter are attracted by any substance on which they fall so as to be diverted from their natural straight course. He succeeded in demonstrating the laws above-mentioned upon that hypothesis, but not so as to set the question at rest. Other philosophers, probably with more truth, have supposed light to consist in undulations, or pulses propagated in a very rare and elastic medium which is supposed to pervade all space, and perhaps to have an intimate connexion with the electro-magnetic fluid.
The action of light is by no means instantaneous. It has been discovered by means of observations on eclipses of Jupiter's satellites, that light takes eight minutes, thirteen seconds of time, to come from the Sun to the Earth.
​It will perhaps be as well to detail an experiment by which the Laws of Optics may be well illustrated.
Let a square or rectangle $AB$ (Fig. 1.) of wood, or any other convenient material, have its opposite sides bisected by lines $CD$, $EF$, and be correctly graduated along the top and bottom, so that the divisions, which must be equal on both lines, may be aliquot, parts tenths or hundredths, for instance, of $GC$ or $GD$.
Let this rectangle be immersed vertically in water up to the line $EF$ in a dark room, so that a small beam of Sun-light admitted through a shutter may just shine along its surface in a line $OG$.
There will then be observed a reflected beam along a line $GP$ on the surface of the rectangle, and a refracted one $GQ$ down through the water, also lying just along the surface of the rectangle. Now if the distances $OC,CP,DQ$ be observed, it will be found that $OC$ and $CP$ are equal, and that $OC$ and $DQ$, which are respectively the tangents of the angles $OGC$, $DGQ$ to the radius $GE$ or $GD$ are so related, that if the sines of the same angles be calculated by the formula ${\frac {\tan }{\sqrt {\mathrm {rad} ^{2}+\tan ^{2}}}}\times \mathrm {rad}$, these sines will be found to be in a certain ratio which in the case of pure water is about that of 4 to 3, or more correctly, 1,336 to 1. The experiment should be repeated several times when the Sun is at different heights, and the ratio of the sines of the angles $OGC$, $DGQ$ will be found invariably the same.
The fact of the incident, reflected, and refracted rays, $GO$, $GP$ and $GQ$, all lying precisely along the same plane surface, shows that those rays are all in the same plane, which is one circumstance mentioned in the Laws.
It may be necessary to observe that it is indifferent as to the directions of connected rays, which way the light is proceeding, that is, whether forwards or backwards, as any causes that act to produce a deflection from the straight course in the one case, would produce corresponding effects in the other.