Although geometrical optics is just an approximation, it is of very gre importance technically and of great interest historically. We shall present this ubject more historically than some of the others in order to give some idea of the development of a physical theory or physical idea tIll irst. light is, of course, familiar to everybody, and has been familiar since immemorial. Now one problem is, by what process do we see light?There have been many theories, but it finally settled down to one, which is that there is something which enters the eyewhich bounces off objects into the eye. We have eard that idea so long that we accept it, and it is almost impossible for us to ealize that very intelligent men have proposed contrary theories-that somethi omes out of the eye and feels for the object, for example. Some other important observations are that, as light goes from one place to another, it goes in straight lines, if there is nothing in the way, and that the rays do not seem to interfere with one another. That is, light is crisscrossing in all directions in the room, but the light that is passing across our line of vision does not affect the light that comes to us from some object. This was once a most powerful argument against the corpuscular theory; it was used by Huygens. If light were like a lot of arro shooting along, how could other arrows go through them so easily? Such philo sophical arguments are not of much weight. One could always say that light is made up of arrows which go through each other! 26-2 Refection and refraction The discussion above gives enough of the basic idea of geometrical optics- now we have to go a little further into the quantitative features. Thus far we have light going only in straight lines between two points; now let us study the behavior of light when it hits various materials. The simplest object is a mirror, and the law for a mirror is that when the light hits the mirror it does not continue in a straight line, but bounces off the mirror into a new straight line, which changes ig.26-1. The angle of incidence is when we change the inclination of the mirror. The question for the ancients was equal to the angle of refection what is the relation between the two angles involved? This is a very simple relation he light striking a mi angles, between each beam and the mirror, are equal. For some reason it is ustomary to measure the angles from the normal to the mirror surface Thus the So-called law of reflection is That is a simple enough proposition, but a more difficult problem is encoun- tered when light goes from one medium into another, for example from air into water;here also, we see that it does not go in a straight line. In the water the ray is at an inclination to its path in the air; if we change the angle i so that it comes down more nearly vertically, then the angle of"breakage"is not as great.But Fig. 26-2. A light ray is refracted if we tilt the beam of light at quite an angle, then the deviation angle is very large when it passes from one medium into The question is, what is the relation of one angle to the other? This also puzzled he ancients for a long time, and here they never found the answer! It is, however one of the few places in all of Greek physics that one may find any experimental Table 26-1 results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26-1 shows the angles in the air, in degrees Angle in air Angle in water and the corresponding angle as measured in the water. ( Ordinarily it is said that Greek scientists never did any experiments. But it would be impossible to obtain this table of values without knowing the right law, except by experiment. It 15-1/2° should be noted, however, that these do not represent independent careful measure 22-1/2° ments for each angle but only some numbers interpolated from a few measure ments,for they all fit perfectly on a parabola. This, then, is one of the important steps in the development of physical law 45-1/2 first we observe an effect, then we measure it and list it in a table; then we try to find the rule by which one thing can be connected with another. The above numerical table was made in 140 A.D. but it was not until 1621 that someone finally found the rule connecting the two angles! The rule, found by Willebrord