Fig. 123

a

In all cases where the ray passes out of a rarer into a denser medium, it is refracted towards a perpendicular line, raised from the surface of the denser medium, and so, when it passes out of a denser, into a rarer medium, it is refracted from the same perpendicular.

b

Let the medium b, fig. 123, be glass, and the medium c, water. The ray a, as it falls upon the medium b, is refracted towards the perpendicular line e, d; but when it enters the water, whose refractive power is less than that of glass, it is not bent so near the perpendicular as before, 9 and hence it is refracted from, instead of towards the perpendicular line, and approaches the original direction of the ray a, g, when passing through the air.

The cause of refraction appears to be the power of attraction, which the denser medium exerts on the passing ray and in all cases the attracting force acts in the direction of a perpendicular to the refracting surface.

The refraction of the rays of light, as they fall upon the surface of the water, is the reason why a straight rod, with one end in the water and the other end rising above it, appears to be broken, or bent, and also to be shortened.

Fig. 124.

Suppose the rod a, fig. 124, to be set with one half of its length below the surface of the water, and the other half above it. The eye being placed in an oblique direction, will see the lower end apparently at the point o, while the real termination of the rod would be at n: the refraction will therefore make the rod appear shorter by the distance from o to n, or one fourth shorter than the part below the water really is. The reason why the rod appears distorted, or broken, is, that we judge of the direction of the part which is under the water, by that which is above it, and the refraction of the rays coming from below the surface of the water, give them a different direction, when compared with those coming from that part of the rod which is above it. Hence, when

When the ray passes out of a rarer into a denser medium, in what direction is it refracted? When it passes out of a denser into a rarer medium, in what direction is the refraction? Explain this by fig. 123. What is the cause of refraction? What is the reason that a rod, with one end in the water, appears distorted and shorter than it really is?

the whole rod is below the water, no such distorted appearance is observed, because then all the rays are refracted equally.

For the reason just explained, persons are often deceived in respect to the depth of water, the refraction making it appear much more shallow than it really is; and there is no doubt but the most serious accidents have often happened to those who have gone into the water under such deception. for a pond which is really six feet deep, will appear to the eye only a little more than four feet deep.

Reflection of Light.

If a boy throws his ball against the side of a house swiftly, and in a perpendicular direction, it will bound back nearly in the line in which it was thrown, and he will be able to catch it with his hands; but if the ball be thrown obliquely to the right, or left, it will bound away from the side of the house in the same relative direction in which it was thrown.

The reflection of light, so far as regards the line of approach, and the line of leaving a reflecting surface, is governed by the same law

Fig. 125.

H

But if the ray
Fig. 126.

K

a

Thus, if a sun beam, fig. 125, passing through a small aperture in the window shutter a, be permitted to fall upon the plane mirror, or looking glass, c, d, at right angles, it will be reflected back at right angles with the mirror, and therefore will pass back again in exactly the same direction in which it approached.

strikes the mirror in an oblique direction, it will also be thrown off in an oblique direction opposite to that in which it was thrown.

Let a ray pass towards a mirror in the line a, c, fig. 126, it will be reflected off in the direction of c, d, making the angles 1 and 2 exactly equal.

The ray a, c, is called the incident ray, and the ray c, d, the reflected ray; and it is found in all cases, that whatever angle the ray of incidence makes with the reflectWhy does the water in a pond appear less deep than it really is? Suppose a sun beam fall upon a plane mirror at right angles with its surface, in what direction will it be reflected? Suppose the ray falls obliquely on its surface, in what direction will it then be reflected? What is an incident ray of light? What is a reflected ray of light?

Fig. 127.

K

ing surface, or with a perpendicular line drawn from the reflecting surface, exactly the same angle is made by the reflected ray.

From these facts, arise the general law in optics, that the angle of reflection is equal to the angle of incidence.

The ray a, c, fig. 127, is the ray of incidence, and that from c to d, is the ray of reflection. The angles which a, c, make with the perpendicular line, and with the plane of the mirror, is exactly equal to those made by c, d, with the same perpendicular, and the same plane surface.

Mirrors.

Mirrors are of three kinds, namely, plane, convex, and concave. They are made of polished metal, or of glass covered on the back with an amalgam of tin and quicksilver.

The common looking glass is a plane mirror, and consists of a plate of ground glass so highly polished as to permit the rays of light to pass through it with little interruption. On the back of this plate is placed the reflecting surface, which consists of a mixture of tin and mercury. The glass plate, therefore, only answers the purpose of sustaining the metallic surface in its place,-of admitting the rays of light to, and from it, and of preventing its surface from tarnishing, by excluding the air. Could the metallic surface, however, be retained in its place, and not exposed to the air without the glass plate, these mirrors would be much more perfect than they are, since, in practice, glass cannot be made so perfect as to transmit all the rays of light which fall on its surface.

When applied to the plane mirror, the angles of incidence and of reflection are equal, as already stated, and it therefore follows, that when the rays of light fall upon it obliquely in one direction, they are thrown off under the same angle in the opposite direction.

This is the reason why the images of objects can be seen when the objects themselves are not visible.

What general law in optics results from observations on the incident and reflected rays? How many kinds of mirrors are there? What kind of mirror is the common looking glass? Of what use is the glass plate in the construction of this mirror?

a

Fig. 128.

We

Suppose the mirror a b, fig. 128, to be placed on the side of a room, and a lamp to be set in another room, but so situated, as that its light would shine upon the glass. The lamp itself could not be d seen by the eye placed at e, because the partition d is between them; but its image would be visible at e, because the angle of the incident ray, coming from the light, and that of the reflected ray which reaches the eye, are equal.

An image from a plane mirror appears to be just as far behind the mirror, as the object is before it, so that when a person approaches this mirror, his image seems to come forward to meet him; and when he withdraws from it, his image appears to be moving backward at the same rate. For the same reason the different parts of the same object will appear to extend as far behind the mirror, as they are before it.

If, for instance, one end of a rod two feet long be made to touch the surface of such a mirror, this end of the rod, and its image, will seem nearly to touch each other, there being only the thickness of the glass between them; while the other end of the rod, and the other end of its image, will appear to be equally distant from the point of contact.

The reason of this is explained on the principle, that the angle of incidence and that of reflection is equal.

Fig. 129.

h

Suppose the arrow a, to be the object reflected by the mirror d c fig. 129; the incident rays a. flowing from the end of the ar row, being thrown back by reflection, will meet the eye in the same state of divergence that they would do, if they proceeded to the same distance behind the mirror, that the eye is before it, Therefore, by the same

as at o.

Explain fig. 128, and show how the image of an object can be seen in a plane mirror, when the real object is invisible. The image of an object appears just as far behind a plane mirror, as the object is before it; explain fig 129, and show why this is the case.

law, the reflected rays, where they meet the eye at e, appear to diverge from a point h, just as far behind the mirror, as a is before it, and consequently the end of the arrow most remote from the glass, will appear to be at h, or the point where the approaching rays would meet, were they continued onward behind the glass. The rays flowing from every other part of the arrow follow the same law; and thus every part of the image seems to be at the same distance behind the mirror, that the object really is before it.

In a plane mirror, a person may see his whole image, when the mirror is only half as long as himself; let him stand at any distance from it whatever.

This is also explained by the law, that the angles of incidence and reflection are equal. If the mirror be elevated, so that the ray of light from the eye falls perpendicularly upon the mirror, this ray will be thrown back by reflection in the same direction, so that the incident and reflected ray by which the image of the eyes and face are formed, will be nearly pa rallel, while the ray flowing from his feet will fall on the mirror obliquely, and will be reflected as obliquely in the contrary direction, and so of all the other rays by which the image of the different parts of the person is formed.

Fig. 130.

Thus suppose the mira ror c e, fig. 130, to be just half as long as the arrow placed before it, and suppose the eye to be placed at a. Then the ray a e, proceeding from the eye at a, and falling perpendicularly on the glass at c, will be reflected back to the eye in the same line, and this part of the image will appear at b, in the same line, and at the same distance behind the glass that the arrow is before it. But the ray flowing from the lower extremity of the arrow, will fall on the mirror obliquely, as at e, and will be reflected under the same angle to the eye, and therefore the extremity of the

What must be the comparative length of a plane mirror, in which a person may see his whole image? In what part of the image, fig. 130, are the incidental and reflected rays nearly parallel? Why does the image of the lower part of the arrow appear at d?