different situations, which must be owing to an image of it being formed
on each eye; if the action of the rays, therefore, on each retina, were
not so perfectly similar as to produce but one sensation, we should see
double; and we find that to be the case with some persons, who are
afflicted with a disease in one eye, which prevents the rays of light
from affecting it in the same manner as the other.
_Emily._ Pray, Mrs. B., when we see the image of an object in a
looking-glass, why is it not inverted, as in the camera obscura, and on
the retina of the eye?
_Mrs. B._ Because the rays do not enter the mirror by a small aperture,
and cross each other, as they do at the orifice of a camera obscura, or
the pupil of the eye.
When you view yourself in a mirror, the rays from your eyes fall
perpendicularly upon it, and are reflected in the same line; the image
is, therefore, described behind the glass, and is situated in the same
manner as the object before it.
_Emily._ Yes, I see that it is; but the looking-glass is not nearly so
tall as I am, how is it, therefore, that I can see the whole of my
figure in it?
_Mrs. B._ It is not necessary that the mirror should be more than half
your height, in order that you may see the whole of your person in it,
(fig. 3.) The ray of light A B, from your eye, which falls
perpendicularly on the mirror B D, will be reflected back, in the same
line; but the ray from your feet, will fall obliquely on the mirror, for
it must ascend in order to reach it; it will, therefore, be reflected in
the line A D: and since we view objects in the direction of the
reflected rays, which reach the eye, and since the image appears at the
same distance, behind the mirror, that the object is before it, we must
continue the line A D to E, and the line C D to F, at the termination of
which, the image will be represented.
[Illustration: PLATE XVIII.]
_Emily._ Then I do not understand why I should not see the whole of my
person in a much smaller mirror, for a ray of light from my feet would
always reach it, though more obliquely.
_Mrs. B._ True; but the more obliquely the ray falls on the mirror, the
more obliquely it will be reflected; the ray would, therefore, be
reflected above your head, and you could not see it. This is shown by
the dotted line (fig. 3.)
Now stand a little to the right of the mirror, so that the rays of light
from your figure may fall obliquely on it----
_Emily._ There is no image formed of me in the glass now.
_Mrs. B._ I beg your pardon, there is; but you cannot see it, because
the incident rays, falling obliquely on the mirror, will be reflected
obliquely, in the opposite direction; the angles of incidence, and
reflection, being equal. Caroline, place yourself in the direction of
the reflected rays, and tell me whether you do not see Emily's image in
the glass?
_Caroline._ Let me consider.--In order to look in the direction of the
reflected rays, I must place myself as much to the left of the glass, as
Emily stands to the right of it.--Now I see her image, not straight
before me, however, but before her; and it appears at the same distance
behind the glass, that she is in front of it.
_Mrs. B._ You must recollect, that we always see objects in the
direction of the last rays, which reach our eyes. Figure 4 represents an
eye, looking at the image of a vase, reflected by a mirror; it must see
it in the direction of the ray A B, as that is the ray which brings the
image to the eye; prolong the ray to C, and in that spot will the image
appear.
_Caroline._ I do not understand why a looking-glass reflects the rays of
light; for glass is a transparent body, which should transmit them!
_Mrs. B._ It is not the glass that reflects the rays which form the
image you behold, but the silvering behind it; this silvering is a
compound of mercury and tin, which forms a brilliant metallic coating.
The glass acts chiefly as a transparent case, through which the rays
find an easy passage, to, and from, the quicksilver.
_Caroline._ Why then should not mirrors be made simply of mercury?
_Mrs. B._ Because mercury is a fluid. By amalgamating it with tinfoil,
it becomes of the consistence of paste, attaches itself to the glass,
and forms, in fact, a metallic mirror, which would be much more perfect
without its glass cover, for the purest glass is never perfectly
transparent; some of the rays, therefore, are lost during their passage
through it, by being either absorbed, or irregularly reflected.
This imperfection of glass mirrors, has introduced the use of metallic
mirrors, for optical purposes.
_Emily._ But since all opaque bodies reflect the rays of light, I do not
understand why they are not all mirrors.
_Caroline._ A curious idea indeed, sister; it would be very gratifying
to see oneself in every object at which one looked.
_Mrs. B._ It is very true that all opaque objects reflect light; but the
surface of bodies, in general, is so rough and uneven, that the
reflection from them is extremely irregular, and prevents the rays from
forming an image on the retina. This, you will be able to understand
better, when I shall explain to you the nature of vision, and the
structure of the eye.
You may easily conceive the variety of directions in which rays would be
reflected by a nutmeg-grater, on account of the inequality of its
surface, and the number of holes with which it is pierced. All solid
bodies more or less resemble the nutmeg-grater, in these respects; and
it is only those which are susceptible of receiving a polish, that can
be made to reflect the rays with regularity. As hard bodies are of the
closest texture, the least porous, and capable of taking the highest
polish, they make the best mirrors; none, therefore, are so well
calculated for this purpose, as metals.
_Caroline._ But the property of regular reflection, is not confined to
this class of bodies; for I have often seen myself, in a highly polished
mahogany table.
_Mrs. B._ Certainly; but as that substance is less durable, and its
reflection less perfect, than that of metals, I believe it would seldom
be chosen, for the purpose of a mirror.
There are three kinds of mirrors used in optics; the _plain_, or _flat_,
which are the common mirrors we have just mentioned; _convex_ mirrors,
and _concave_ mirrors. The reflection of the two latter, is very
different from that of the former. The plain mirror, we have seen, does
not alter the direction of the reflected rays, and forms an image behind
the glass, exactly similar to the object before it. A convex mirror has
the peculiar property of making the reflected rays diverge, by which
means it diminishes the image; and a concave mirror makes the rays
converge, and under certain circumstances, magnifies the image.
_Emily._ We have a convex mirror in the drawing-room, which forms a
beautiful miniature picture of the objects in the room; and I have often
amused myself with looking at my magnified face in a concave mirror. But
I hope you will explain to us, why the one enlarges, while the other
diminishes the objects it reflects.
_Mrs. B._ Let us begin by examining the reflection of a convex mirror.
This is formed of a portion of the exterior surface of a sphere. When
several parallel rays fall upon it, that ray only which, if prolonged,
would pass through the centre or axis of the mirror, is perpendicular to
it. In order to avoid confusion, I have, in fig. 1, plate 18, drawn only
three parallel lines, A B, C D, E F, to represent rays falling on the
convex mirror, M N; the middle ray, you will observe, is perpendicular
to the mirror, the others fall on it, obliquely.
_Caroline._ As the three rays are parallel, why are they not all
perpendicular to the mirror?
_Mrs. B._ They would be so to a flat mirror; but as this is spherical,
no ray can fall perpendicularly upon it which is not directed towards
the centre of the sphere.
_Emily._ Just as a weight falls perpendicularly to the earth, when
gravity attracts it towards the centre.
_Mrs. B._ In order, therefore, that rays may fall perpendicularly to the
mirror at B and F, the rays must be in the direction of the dotted
lines, which, you may observe, meet at the centre O of the sphere, of
which the mirror forms a portion.
Now, can you tell me in what direction the three rays, A B, C D, E F,
will be reflected?
_Emily._ Yes, I think so: the middle ray, falling perpendicularly on the
mirror, will be reflected in the same line: the two outer rays falling
obliquely, will be reflected obliquely to G and H; for the dotted lines
you have drawn are perpendiculars, which divide the angles of incidence
and reflection, of those two rays.
_Mrs. B._ Extremely well, Emily: and since we see objects in the
direction of the reflected ray, we shall see the image L, which is the
point at which the reflected rays, if continued through the mirror,
would unite and form an image. This point is equally distant, from the
surface and centre of the sphere, and is called the imaginary focus of
the mirror.
_Caroline._ Pray, what is the meaning of focus?
_Mrs. B._ A point at which converging rays, unite. And it is in this
case, called an imaginary focus; because the rays do not really unite at
that point, but only appear to do so: for the rays do not pass through
the mirror, since they are reflected by it.
_Emily._ I do not yet understand why an object appears smaller, when
viewed in a convex mirror.
_Mrs. B._ It is owing to the divergence of the reflected rays. You have
seen that a convex mirror, by reflection, converts parallel rays into
divergent rays; rays that fall upon the mirror divergent, are rendered
still more so by reflection, and convergent rays are reflected either
parallel, or less convergent. If then, an object be placed before any
part of a convex mirror, as the vase A B, fig. 2, for instance, the two
rays from its extremities, falling convergent on the mirror, will be
reflected less convergent, and will not come to a focus, till they
arrive at C; then an eye placed in the direction of the reflected rays,
will see the image formed in (or rather behind) the mirror, at _a b_.
_Caroline._ But the reflected rays, do not appear to me to converge less
than the incident rays. I should have supposed that, on the contrary,
they converged more, since they meet in a point.
_Mrs. B._ They would unite sooner than they actually do, if they were
not less convergent than the incident rays: for observe, that if the
incident rays, instead of being reflected by the mirror, continued their
course in their original direction, they would come to a focus at D,
which is considerably nearer to the mirror than at C; the image, is,
therefore, seen under a smaller angle than the object; and the more
distant the latter is from the mirror, the smaller is the image
reflected by it.
You will now easily understand the nature of the reflection of concave
mirrors. These are formed of a portion of the internal surface of a
hollow sphere, and their peculiar property is to converge the rays of
light.
Can you discover, Caroline, in what direction the three parallel rays, A
B, C D, E F, are reflected, which fall on the concave mirror, M N, (fig.
3.)?
_Caroline._ I believe I can. The middle ray is sent back in the same
line, in which it arrives, that being the direction of the axis of the
mirror; and the two others will be reflected obliquely, as they fall
obliquely on the mirror. I must now draw two dotted lines perpendicular
to their points of incidence, which will divide their angles of
incidence and reflection; and in order that those angles may be equal,
the two oblique rays must be reflected to L, where they will unite with
the middle ray.
_Mrs. B._ Very well explained. Thus you see, that when any number of
parallel rays fall on a concave mirror, they are all reflected to a
focus: for in proportion as the rays are more distant from the axis of
the mirror, they fall more obliquely upon it, and are more obliquely
reflected; in consequence of which they come to a focus in the direction
of the axis of the mirror, at a point equally distant from the centre,
and the surface, of the sphere; and this point is not an imaginary
focus, as happens with the convex mirror, but is the true focus at which
the rays unite.
_Emily._ Can a mirror form more than one focus, by reflecting rays?
_Mrs. B._ Yes. If rays fall convergent on a concave mirror, (fig. 4,)
they are sooner brought to a focus, L, than parallel rays; their focus
is, therefore, nearer to the mirror M N. Divergent rays are brought to a
more distant focus than parallel rays, as in figure 5, where the focus
is at L; but what is called the true focus of mirrors, either convex or
concave, is that of parallel rays, and is equally distant from the
centre, and the surface of the spherical mirror.
I shall now show you the real reflection of rays of light, by a metallic
concave mirror. This is one made of polished tin, which I expose to the
sun, and as it shines bright, we shall be able to collect the rays into
a very brilliant focus. I hold a piece of paper where I imagine the
focus to be situated; you may see by the vivid spot of light on the
paper, how much the rays converge: but it is not yet exactly in the
focus; as I approach the paper to that point, observe how the brightness
of the spot of light increases, while its size diminishes.
_Caroline._ That must be occasioned by the rays approaching closer
together. I think you hold the paper just in the focus now, the light is
so small and dazzling--Oh, Mrs. B., the paper has taken fire!
_Mrs. B._ The rays of light cannot be concentrated, without, at the same
time, accumulating a proportional quantity of heat: hence concave
mirrors have obtained the name of burning mirrors.
_Emily._ I have often heard of the surprising effects of burning
mirrors, and I am quite delighted to understand their nature.
_Caroline._ It cannot be the true focus of the mirror, at which the
rays of the sun unite, for as they proceed from so large a body, they
cannot fall upon the mirror parallel to each other.
_Mrs. B._ Strictly speaking, they certainly do not. But when rays, come
from such an immense distance as the sun, they may be considered as
parallel: their point of union is, therefore, the true focus of the
mirror, and there the image of the object is represented.
Now that I have removed the mirror out of the influence of the sun's
rays, if I place a burning taper in the focus, how will its light be
reflected? (Fig. 6.)
_Caroline._ That, I confess, I cannot say.
_Mrs. B._ The ray which falls in the direction of the axis of the
mirror, is reflected back in the same line; but let us draw two other
rays from the focus, falling on the mirror at B and F; the dotted lines
are perpendicular to those points, and the two rays will, therefore, be
reflected to A and E.
_Caroline._ Oh, now I understand it clearly. The rays which proceed from
a light placed in the focus of a concave mirror fall divergent upon it,
and are reflected, parallel. It is exactly the reverse of the former
experiment, in which the sun's rays fell parallel on the mirror, and
were reflected to a focus.
_Mrs. B._ Yes: when the incident rays are parallel, the reflected rays
converge to a focus; when, on the contrary, the incident rays proceed
from the focus, they are reflected parallel. This is an important law of
optics, and since you are now acquainted with the principles on which it
is founded, I hope that you will not forget it.
_Caroline._ I am sure that we shall not. But, Mrs. B., you said that the
image was formed in the focus of a concave mirror; yet I have frequently
seen glass concave mirrors, where the object has been represented within
the mirror, in the same manner as in a convex mirror.
_Mrs. B._ That is the case only, when the object is placed between the
mirror and its focus; the image then appears magnified behind the
mirror, or, as you would say, within it.
_Caroline._ I do not understand why the image should be larger than the
object.
_Mrs. B._ This results from the convergent property of the concave
mirror. If an object, A B, (fig. 7.) be placed between the mirror and
its focus, the rays from its extremities fall divergent on the mirror,
and on being reflected, become less divergent, as if they proceeded from
C: to an eye placed in that situation, the image will appear magnified
behind the mirror at _a b_, since it is seen under a larger angle than
the object.
You now, I hope, understand the reflection of light by opaque bodies. At
our next meeting, we shall enter upon another property of light, no less
interesting, and which is called _refraction_.
Questions
1. (Pg. 168) What is meant by the angle of vision, or the visual angle?
2. (Pg. 169) Why do objects of the same size appear smaller when
distant, than when near?
3. (Pg. 169) Why do not two objects, known to be equal in size, appear
to differ, when at different distances from the eye?
4. (Pg. 169) How is this exemplified, by a house seen through a window?
5. (Pg. 170) Why do rows of trees, forming an avenue, appear to approach
as they recede from the eye, until they eventually seem to meet?
6. (Pg. 170) In drawing a view from nature, what do we copy?
7. (Pg. 170) What is the difference in sculpture, in this respect?
8. (Pg. 170) Excepting the rays from an object enter the eye, under a
certain angle, they cannot be seen; what must this angle exceed?
9. (Pg. 170) What two circumstances may cause the angle to be so small,
as not to produce vision?
10. (Pg. 170) Motion may be so slow as to become imperceptible, what is
said on this point?
11. (Pg. 170) Under what circumstances may a body, moving with great
rapidity, appear to be at rest?
12. (Pg. 170) Upon what does the real velocity of a body, depend?
13. (Pg. 171) What must be known, to enable us to ascertain the real
space contained in a degree?
14. (Pg. 171) What is explained by fig. 2, plate 17?
15. (Pg. 171) What is said respecting the evidence afforded by our
senses, and how do we correct the errors into which they would lead us?
16. (Pg. 171) An image of a visible object is formed upon the retina of
each eye, why, therefore, are not objects seen double?
17. (Pg. 172) By what experiment can you prove that a separate image of
an object is formed in each eye?
18. (Pg. 172) Under what circumstances are objects seen double?
19. (Pg. 172) Why is not the image of an object inverted in the common
mirror?
20. (Pg. 172) Your whole figure may be seen in a looking-glass, which is
not more than half your height; how is this shown in fig. 3. plate 17?
21. (Pg. 173) Why is the image invisible to the person, when not
standing directly before the glass?
22. (Pg. 173) In what situation may a second person see the image
reflected?
23. (Pg. 173) In what direction will an object always appear to the eye?
24. (Pg. 173) How is this explained by fig. 4, plate 17?
25. (Pg. 173) What is it that reflects the rays in a looking-glass?
26. (Pg. 174) All opaque bodies reflect some light, why do they not all
act as mirrors?
27. (Pg. 174) What substances form the most perfect mirrors, and for
what reason?
28. (Pg. 174) What are the three kinds of mirrors usually employed for
optical purposes?
29. (Pg. 174) How are the rays of light affected by them?
30. (Pg. 175) What is the form of a convex mirror, and how do parallel
rays fall upon it, as represented in fig. 1, plate 18?
31. (Pg. 175) What is represented by the dotted line in the same figure?
32. (Pg. 175) Explain by the figure, how the parallel rays will be
reflected.
33. (Pg. 175) At what distance behind such a mirror, would an image,
produced by parallel rays, be formed?
34. (Pg. 175) What is that point denominated?
35. (Pg. 176) What is meant by a focus?
36. (Pg. 176) Why is the point behind the mirror, called the _imaginary
focus_?
37. (Pg. 176) Why does an object appear to be lessened by a convex
mirror, (fig. 2.)?
38. (Pg. 176) What is a concave mirror, and what its peculiar property?
39. (Pg. 176) How are parallel rays reflected by a concave mirror, as
explained by fig. 3, plate 18?
40. (Pg. 177) Where is the focus of parallel rays, in a concave mirror?
41. (Pg. 177) If rays fall on it convergent, how are they reflected?
42. (Pg. 177) How if divergent?
43. (Pg. 177) How, and why, may concave, become burning mirrors?
44. (Pg. 178) Why may rays of light coming from the sun, be viewed as
parallel to each other?
45. (Pg. 178) If a luminous body, as a burning taper, be placed in the
focus of a concave mirror, how will the rays from it, be reflected?
(fig. 6.)
46. (Pg. 178) What fact is explained by fig. 7, plate 18?
CONVERSATION XVI.
ON REFRACTION AND COLOURS.
TRANSMISSION OF LIGHT BY TRANSPARENT BODIES. REFRACTION. REFRACTION BY
THE ATMOSPHERE. REFRACTION BY A LENS. REFRACTION BY THE PRISM. OF COLOUR
FROM THE RAYS OF LIGHT. OF THE COLOURS OF BODIES.
MRS. B.
The refraction of light will furnish the subject of to-day's lesson.
_Caroline._ That is a property of which I have not the faintest idea.
_Mrs. B._ It is the effect which transparent mediums produce on light in
its passage through them. Opaque bodies, you know, reflect the rays, and
transparent bodies transmit them; but it is found, that _if a ray, in
passing from one medium, into another of different density, fall
obliquely, it is turned out of its course. The ray of light is then said
to be refracted._
_Caroline._ It must then be acted on by some new power, otherwise it
would not deviate from its first direction.
_Mrs. B._ The power which causes the deviation of the ray, appears to be
the attraction of the denser medium. Let us suppose the two mediums to
be air, and water; if a ray of light passes from air, into water, it is
more strongly attracted by the latter, on account of its superior
density.
_Emily._ In what direction does the water attract the ray?
_Mrs. B._ The ray is attracted perpendicularly towards the water, in
the same manner in which bodies are acted upon by gravity.
If then a ray, A B, (fig. 1, plate 19.) fall perpendicularly on water,
the attraction of the water acts in the same direction as the course of
the ray: it will not, therefore, cause a deviation, and the ray will
proceed straight on, to E. But if it fall obliquely, as the ray C B, the
water will attract it out of its course. Let us suppose the ray to have
approached the surface of a denser medium, and that it there begins to
be affected by its attraction; this attraction, if not counteracted by
some other power, would draw it perpendicularly to the water, at B; but
it is also impelled by its projectile force, which the attraction of the
denser medium cannot overcome; the ray, therefore, acted on by both
these powers, moves in a direction between them, and instead of pursuing
its original course to D, or being implicitly guided by the water to E,
proceeds towards F, so that the ray appears bent or broken.
_Caroline._ I understand that very well; and is not this the reason that
oars appear bent in the water?
_Mrs. B._ It is owing to the refraction of the rays, reflected by the
oar; but this is in passing from a dense, to a rare medium, for you know
that the rays, by means of which you see the oar, pass from water into
air.
_Emily._ But I do not understand why refraction takes place, when a ray
passes from a dense into a rare medium; I should suppose that it would
be less, attracted by the latter, than by the former.
_Mrs. B._ And it is precisely on that account that the ray is refracted.
Let the upper half of fig. 2, represent glass, and the lower half water,
let C B represent a ray, passing obliquely from the glass, into water:
glass, being the denser medium, the ray will be more strongly attracted
by that which it leaves than by that which it enters. The attraction of
the glass acts in the direction A B, while the impulse of projection
would carry the ray to F; it moves, therefore, between these directions
towards D.
_Emily._ So that a contrary refraction takes place, when a ray passes
from a dense, into a rare medium.
[Illustration: PLATE XIX.]
_Mrs. B._ The rule upon this subject is this; _when a ray of light
passes from a rare into a dense medium, it is refracted towards the
perpendicular; when from a dense into a rare medium, it is refracted
from the perpendicular_. By the perpendicular is meant a line, at right
angle with the refracting surface. This may be seen in fig. 1, and
fig. 2, where the lines A E, are the perpendiculars.
_Caroline._ But does not the attraction of the denser medium affect the
ray before it touches it?
_Mrs. B._ The distance at which the attraction of the denser medium acts
upon a ray, is so small, as to be insensible; it appears, therefore, to
be refracted only at the point at which it passes from one medium into
the other.