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bottle to the dark room. Place it nearer to the mirror, and let the reflected beam of light fall upon it at a different angle, being careful that the beam strikes the water at the centre of the circle. Examine the beam of light in the bottle, and you will observe that it is bent, but at a different angle. Mark the two points where the beam crosses the circle above and below the water, and measure their distances from the perpendicular line, and then compare these distances with those we obtained the first time. Divide the distance between A and B by the distance between C and D, and you will obtain a certain quotient. Divide the two sets of figures obtained the second time (that is, the distance from the edge of the circle to the perpendicular line above by the same below the water), and the quotient or ratio of the one to the other will be exactly the same as before. For instance, if the distance from A to B is four units, the distance from C to D will be three units, and in every experiment this proportion will be the same. In this case, where the light passes from the air to the water, we get a quotient that is one and a third, and this quotient we call the index of refraction. These experiments show us that there is a fixed law of refraction. When the light met the surface of the water at a right angle, it passed

through the water without bending. In such instances the light is said to meet the water in a normal direction. If it meets the water on either side of this normal, it is refracted. Glass, diamonds, mica, and every transparent substance, have their own peculiar refraction. Glass has an index of refraction of 1.5. A diamond has quite another index of refraction,

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and it is by comparing these that we are able to prove whether a stone is a real diamond or only an imitation made of glass.

Above is a picture representing the bottle in a new position. The beam of sunlight enters the darkened window, and falls upon a mirror lying flat on the

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

-B

X

FIG. 18.

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 O 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.

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