CHAPTER II.
ON THE REFRACTION OF LIGHT.
Refraction is the turning or bending of the rays of light out of their natural course.
Light, when proceeding from a luminous body—without being reflected from any opake substance or inflected by passing near one—is invariably found to proceed in straight lines without the least deviation. But if it happens to pass obliquely from one medium to another, it always leaves the direction it had before and assumes a new one. This change of direction, or bending of the rays of light, is what is called Refraction—a term which probably had its origin from the broken appearance which a staff or a long pole exhibits, when a portion of it is immersed in water—the word, derived from the Latin frango, literally signifying breaking or bending.
When light is thus refracted, or has taken a new direction, it then proceeds invariably in a straight line till it meets with a different medium,7 when it is again turned out of its course. It must be observed, however, that though we may by this means cause the rays of light to make any number of angles in their course, it is impossible for us to make them describe a curve, except in one single case, namely, where they pass through a medium, the density of which either uniformly increases or diminishes. This is the case with the light of the celestial bodies, which passes downwards through our atmosphere, and likewise with that which is reflected upwards through it by terrestrial objects. In both these cases it describes a curve of the hyperbolic kind; but at all other times, it proceeds in straight lines, or in what may be taken for straight lines without any sensible error.
There are two circumstances essential to refraction. 1. That the rays of light shall pass out of one medium into another of a different density, or of a greater or less degree of resistance. 2. That they pass in an oblique direction. The denser the refracting medium, or that into which the ray enters, the greater will be its refracting power; and of two refracting mediums of the same density, that which is of an oily or inflammable nature will have a greater refracting power than the other. The nature of refraction may be more particularly explained and illustrated by the following figure and description.
Let ADHI fig. 2, be a body of water, AD its surface, C a point in which a ray of light BC enters from the air into the water. This ray, by the greater density of the water, instead of passing straight forward in its first direction to K, will be bent at the point C, and pass along in the direction CE, which is called the refracted ray. Let the line FG be drawn perpendicular to the surface of the water in C, then it is evident that the ray BC, in passing out of air, a rare medium, into a dense medium, as water, is refracted into a ray CE which is nearer to the perpendicular CG than the incident ray BC, and on the contrary, the ray EC passing out of a denser medium into a rarer will be refracted into CB, which is farther from the perpendicular.
figure 2.
The same thing may be otherwise illustrated as follows:—suppose a hole made in one of the sides of the vessel as at a, and a lighted candle placed within two or three feet of it, when empty, so that its flame may be at L, a ray of light proceeding from it will pass through the hole a in a straight line LBCK till it reach the bottom of the vessel at K, where it will form a small circle of light. Having put a mark at the point K, pour water into the vessel till it rise to the height AD, and the round spot that was formerly at K, will appear at E; that is, the ray which went straight forward, when the vessel was empty, to K, has been bent at the point C, where it falls into the the water, into the line CE. In this experiment it is necessary that the front of the vessel should be of glass, in order that the course of the ray may be seen; and if a little soap be mixed with the water so as to give it a little mistiness, the ray CE will be distinctly perceived. If, in place of fresh water we pour in salt water, it will be found that the ray BC is more bent at C. In like manner alcohol will refract the ray BC more than salt water, and oil more than alcohol, and a piece of solid glass, of the shape of the water, would refract the light still more than the oil.
The angle of refraction depends on the obliquity of the rays falling on the refracting surface being always such, that the sine of the incident angle is to the sine of the refracted angle, in a given proportion. The incident angle is the angle made by a ray of light and a line drawn perpendicular to the refracting surface, at the point where the light enters the surface. The refracted angle is the angle made by the ray in the refracting medium with the same perpendicular produced. The sine of the angle is a line which serves to measure the angle, being drawn from a point in one leg perpendicular to the other. The following figure (fig. 3.) will tend to illustrate these definitions.
figure 3.
In this figure BC is the incident ray, CE the refracted ray, DG the perpendicular, AD the sine of the angle of incidence ACD, and HR the sine of the angle of refraction GCE. Now, it is a proposition in optics that,—the sine AD of the angle of incidence BCD is either accurately or very nearly in a given proportion to the sine HR of the angle of refraction GCE. This ratio of the sines is as four to three, when the refraction is made out of air into water, that is AD is to HR as four to three. When the refraction is out of air into glass, the proportion is about as thirty-one to twenty, or nearly as three to two. If the refraction be out of air into diamond it is as five to two, that is AD : HR :: 5 : 2. The denser the medium is, the less is the angle and sine of refraction. If a ray of light MC, were to pass from air into water, or from empty space into air, in the direction MC perpendicular to the plane NO which separates the two mediums, it would suffer no refraction, because one of the essentials to that effect is wanting, namely, the obliquity of the incidence.
It may be also proper to remark, that a ray of light cannot pass out of a denser medium into a rarer, if the angle of incidence exceed a certain limit. Thus a ray of light will not pass out of glass into air, if the angle of incidence exceed 40° 11´; or out of glass into water, if the angle of incidence exceed 59° 20´. In such cases refraction will be changed into reflection.
The following common experiments, which are easily performed, will illustrate the doctrine of refraction. Put a shilling or any other small object which is easily distinguished, into a bason or any other similar vessel, and then retire to such a distance as that the edge of the vessel shall just hide it from your sight. If then you cause another person to fill the vessel with water, you will then find that the shilling is rendered perfectly visible, although you have not in the slightest degree changed your position. The reason of this is, that the rays of light, by which it is rendered visible, are bent out of their course. Thus, suppose the shilling to have been placed in the bottom of the bason at E, (fig. 2.) the ray of light BC which passes obliquely from the air into water at C, instead of continuing its course to K, takes the direction CE, and consequently an object at E would be rendered visible by rays proceeding in that direction, when they would not have touched it had they proceeded in their direct course.
The same principle is illustrated by the following experiment. Place a bason or square box on a table, and a candle at a small distance from it; lay a small rod or stick across the sides of the bason, and mark the place where the extremity of the shadow falls, by placing a shilling or other object at the point; then let water be poured into the bason, and the shadow will then fall much nearer to the side next the candle than before. This experiment may likewise be performed by simply observing the change produced on the shadow of the side of the bason itself. Again, put a long stick obliquely into deep water, and the stick will seem to be broken at the point where it appears at the surface of the water—the part which is immersed in the water appearing to be bent upwards. Hence every one must have observed that, in rowing a boat, the ends of the oars appear bent or broken every