REFRACTION.
If a straight stick or pencil be plunged into a vessel containing water,
it will appear to be bent. The reason for this appearance is given in
detail in Figure 79. The only light which can reach the eye from the
lower extremity of the stick must reach it by a path similar to that of
the bended ray at the left. According to this, the rays of light leaving
the bottom of the stick at _E_ bend at the water’s edge and meet the eye
as shown. To the eye the rays, by which it sees the end of the stick,
appear to come from the direction _F_; hence the stick is seen crooked.
When a ray of light passes from air into a denser medium such as water
or glass, the ray appears to be bent somewhat, as illustrated at the
left of Figure 79. This bending of the rays of light is called
_refraction_.
[Illustration: FIGURE 79.]
The fact of refraction can be further verified by placing an object _G_
into an empty vessel in the position shown. In this position the object
is not visible to the eye. By slowly filling the vessel with water, the
object will gradually appear and will seem to lie in the direction of
the straight dotted line.
[Illustration: FIGURE 80.]
The bending or refraction of light rays is governed by a law which holds
in all cases. The bending differs with different kinds of glass, with
water, with oils, or even with water mixed with chemicals; but no matter
how much the bending may differ with different materials, for each
material there is a fixed ratio between the angle at which the light
enters and the angle at which it continues in the material. This ratio
is known as the _index of refraction_. For water it is about 1.33; for
glass about 1.5; for the diamond about 2.5; etc. This can perhaps be
most easily explained by reference to Figure 80. Here the top of the
shaded space represents the surface of the glass at which the light
enters. The line _E_ is drawn at right angles to this surface and the
various lines, meeting in the center of the circle, represent different
rays of light falling upon the glass at different angles. The heavy line
shows the ray of light striking the glass and passing through it.
Similarly each line is drawn differently and the nature of the lines
will act as a guide by which the angle of incidence upon the glass and
the angle at which the rays continue through the glass can be traced.
When it is said that glass has an index of refraction of 1.5, or 3/2, it
means that the sine of the angle of incidence is 1.5 times as great as
the sine of the angle of refraction. The sine of the angle of incidence
is proportional to the length of a line drawn from the vertical _E_ to
the periphery of a circle, outside of the glass or other substance, to
where it meets the ray; and the sine of the angle of refraction is
proportional to the length of a line drawn from the same vertical to the
periphery of the same circle, inside of the glass or other substance,
where it meets the ray.
In order to lay out the path of a ray through the material, its angle of
incidence being known, we may resort to the construction shown in Figure
80. Draw the incident ray at its proper angle and the vertical line at
right angles to the surface of the material. From the point _A_, where
the ray enters the circle, and at right angles to the vertical line,
draw the line _1_. Measure the distance from _A_ to the vertical line
and divide it by the index of refraction; and on a continuation of the
line _1_, lay off the distance as found. From the point so located, draw
a line parallel to the vertical until it intersects the circle at the
bottom. From the point at which the ray enters the medium, draw another
line to where the last line drawn strikes the circle. This line will
give the direction in which the ray is propagated in the medium. For
glass, the index of refraction is taken as 3/2; hence the line _1_ must
contain three parts, while the continuation contains two of the same
length. Upon leaving the medium, the ray is bent back again so that it
continues in a direction parallel to that at which it entered, as shown
in Fig. 81; and thus the case is reversed.
[Illustration: FIGURE 81.]
[Illustration: FIGURE 82.]
Figure 82 is an illustration of how both refracted and reflected rays
may be several times reflected. If one will hold a match close to a
mirror, looking at it somewhat from the side, there will be visible six
or eight distinct reflections of it. These will be of different
intensity.
If a source of light has its origin in a medium denser than air, it will
be bent as shown in Figure 83. In such a case some of the rays do not
leave the medium at all but are reflected back into it, as indicated at
the right. The heavy line indicates what is commonly known as the
_critical angle_. This angle varies with different substances and is the
angle at which the refracted ray of light skims along the surface and
does not pass out. All rays emitted at a lower angle are returned back
into the medium. If an electric light were immersed in water, only the
rays of light at the left of the black line would be visible to an eye
outside.
[Illustration: FIGURE 83.]
Figure 84 is an illustration of an equilateral prism. Here we have
refraction on both surfaces and a light placed at _A_ would be seen by
the eye as located at _B_. With prisms it is easily possible to locate a
light so that it may be seen in two positions at the same time.
[Illustration: FIGURE 84.]
Figure 85 shows a double convex lens. Both sides of it are segments of
circles or sections of a sphere. The center of curvature or the radius
of one side is at _A_ and that of the other at _B_. Each minute particle
on the surface of such a part of a sphere may be looked upon as the
surface of a prism, the inclination of it being indicated by a line
drawn at right angles to a line passing from the point through the
center of curvature. This is illustrated in the figure by the short
heavy lines at right angles to the broken lines centering at _A_ and
_B_.
[Illustration: FIGURE 85.]
By using the construction explained with Figure 80 and using for the
left-hand surface the circle of broken lines and for the surface at _E_
the circle of solid lines, we find the path of the ray coming from _C_
to cross the principal optical axis at _A_. A similar construction for a
ray at the lower side of the lens would bring it to the same point and
furthermore all parallel rays would focus at this point. This point is
thus known as the _principal focus of the lens_, and the distance
between this point and the lens is called the _focal length of the
lens_. Every lens has two principal foci, one on either side and at
equal distances from the lens.
[Illustration: FIGURE 86.]
[Illustration: FIGURE 87.]
If, instead of subjecting the lens to parallel rays, we use rays
emanating from a central point on the optical axis, they will come to a
focus at some different point on the other side of the lens, as
illustrated in Figure 86. If the light be placed at the principal focus
of the lens, the rays leaving the lens will be parallel. If the light be
brought nearer the lens, the rays leaving it will spread out as shown in
Figure 87; they will leave the lens in a direction such as to make upon
an observer from in front the impression that they are coming from the
point _C_ behind the lens. If the light be placed beyond the principal
focus of the lens, the rays will converge to a point some distance ahead
of it. This distance varies with the position of the light and the two
points (light on one side and focus on the other) are known as
_conjugate foci of the lens_.
[Illustration: FIGURE 88.]
If an object be projected through a lens as, for instance, the arrow at
the right of Figure 88, it will appear upon a screen placed on the
opposite side, but will be inverted. The reason for this is that the
rays of light striking the lens from the top of the arrow will be
refracted as shown, cross the focal point _F_, and meet those which come
from the same point and pass through the center of the lens in a
straight line; and thus the image of the arrow head will appear at the
bottom; in a similar manner the image of the tail of the arrow will
appear at the top. The flatter the lens, the farther away will be the
point at which the image is formed.
[Illustration: FIGURE 89.]
If such a lens be placed over an object, the light will come to the eye
as shown in Figure 89. The solid lines show the rays by which the eye
receives the light and the broken lines show the direction from which it
appears to come. Thus we see the object much enlarged. A lens used in
this manner is spoken of as a _reading glass_, and the greater the
curvature, the greater its magnifying power.
[Illustration: FIGURE 90.]
[Illustration: FIGURE 91.]
In Figure 90 is illustrated a double concave lens. Parallel rays
entering this lens are scattered by it, as shown. Therefore, if such a
lens be placed over an object, the light from the extremity of the
object will come to the eye as indicated in Figure 91, but will give the
appearance of coming along the lines _H_ and _I_. Thus the object will
be seen much reduced in size. Such lenses are sometimes used by artists
to bring landscapes to a reduced size so that they may be viewed as a
whole more easily.
[Illustration: FIGURE 92.]
The general forms of lenses are shown in Figure 92,
(_a_) Is a plano-convex lens
(_b_) Is a double convex lens
(_c_) Is a convexo-concave lens, or convex meniscus
(_d_) Is a plano-concave lens
(_e_) Is a double concave lens
(_f_) Is a concavo-convex lens, or concave meniscus.