table. It is then reflected upward toward the bottle that stands upon a pile of books. The postal-card is put up as before, and the beam of light passes through the slit and enters the bottle below the surface of the water. Look at the beam of light in the bottle through the circular opening. Instead of passing through the water into the air above the surface,

A

X

FIG. 18.

D

-B

it is bent and turns downward into the water again. If, at first, you do not see this curious effect, raise the mirror slightly, tip it up toward the bottle, and take out some of the books under the bottle till the beam of light enters the bottle, in the direction C O, as in the above drawing. Here the line A B represents

the surface of the water in the bottle, and the line Y X is the perpendicular line in the circle. In this experiment the light must enter the bottle at C and pass to at the surface of the water, and then you will see a most curious phenomenon, the reflection of the light from the surface of the water at O downward to D. To understand this singular matter we must study the diagram.

In the diagram a beam of light is represented as entering the circle at G, and is then refracted to H. Another beam goes from I to J. Dotted lines are drawn from each of these beams to the perpendicular, both above and below the water. You can easily compare the relations of these dotted lines above and below, and you will see that they still preserve the same relation to each other that we discovered in former experiments. First, we must observe that light may pass from air to water, as from G to O and H, or from water to air, as from H to O and G, and the amount of bending will be the same in both cases. In other words, the light takes the same path in going from air to water as when moving from water into the air. A beam of light passing to O, just above the surface of the water, will be refracted as already described. To study this matter further, we must reverse the direction of

the light and cause it to pass from the water to the air. The beam of light entering at C, below the water, passes to 0. Now, if we measure a line from C to the perpendicular O X, we shall find it is too long to be three units, if we call the length of the longest line (O B) that can be drawn from the circumference of the circle to its centre four units. The beam of light entering the water passes to the surface at O, and finds itself a prisoner, and it turns back and dives down into the water again. None of our experiments have shown a more singular result than this. The lines which we have so often drawn perpendicular to the diameter, YX, of the circle, are called sines, and the law of refraction is always thus stated: The sines of the angles of incidence have a constant relation to the sines of the angles of refraction. In the case of light passing from air into water, the ratio of the sines is as 4 to 3; in the case of light passing from air into glass, the ratio of the sines is as 3 to 2.

The beam of light entering the water at C is said to have reached the critical angle A O C, and hence is totally reflected. By this is meant that it has gone beyond the critical point, where the law of the sines comes to an end, and reflection takes the place of re fraction.

Sometimes, when walking along a road on a warm day, you may observe a curious quivering in the air just where the road seems to meet the sky, as it goes over a hill. The objects near this point appear to be distorted and to tremble, or they assume fantastic shapes. Here we have an instance of refraction caused by the heated air just above the surface of the road. The light passing through these layers of unequally-heated air is refracted unequally, and the objects that reflect the light appear distorted. In some instances the refraction may pass the critical angle, and we may see the objects apparently doubled by reflection. Warm, calm days by the sea show the same thing, when distant vessels appear repeated in the sky, or when distant land that is really below the horizon "looms" up and glimmers upon the horizon in trembling headlands. This illusion is called the mirage, and takes place when refraction exceeds the critical angle and becomes reflection.

Fill a clear glass tumbler with water, and put a spoon in it, or dip one finger in the water, and hold it above your head so that you can look into the water from below. You will find that you cannot see through the water up into the air above. The under surface of the water will appear to shine like burnished silver, and the spoon or your finger will be reflected in

it, as in a beautiful mirror. This illustrates total reflection, and shows that in this case all light thrown upward through the water is reflected from its surface. Look into the tumbler from above, and it appears full of clear water. Look into it from below, and it seems as if an opaque sheet of silver rested on the water, and shut out the view of everything above.

Take a small glass tube, and roll up a piece of colored paper or printed paper and slip it inside the tube, and then place the tube in the goblet of water. Hold the goblet in the hand near the eyes, and you can see the paper in the tube through the water. Lower the goblet till you can look down into the water from above, and the tube will appear as if made of silver, and the paper will totally disappear. To vary the experiment, lift the tube up and down in the water, and the paper will appear and disappear in the most surprising manner. This also illustrates total reflection. The light reflected from the paper passes through the glass tube into the water, and is refracted. In certain positions the light passes the critical angle, and is reflected from the outer surface of the glass tube, and fails to reach the eye. Look into the goblet from below, and there is the colored paper pictured by total reflection on the under side of the water.