Part 20

_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.

_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.

Now that you understand the principle of refraction, I will show you the real refraction of a ray of light. Do you see the flower painted at the bottom of the inside of this tea-cup? (Fig. 3.)

_Emily._ Yes.--But now you have moved it just out of sight; the rim of the cup hides it.

_Mrs. B._ Do not stir. I will fill the cup with water, and you will see the flower again.

_Emily._ I do, indeed! Let me try to explain this: when you drew the cup from me, so as to conceal the flower, the rays reflected by it, no longer met my eyes, but were directed above them; but now that you have filled the cup with water, they are refracted, and bent downwards when passing out of the water, into the air, so as again to enter my eyes.

_Mrs. B._ You have explained it perfectly: fig. 3. will help to imprint it on your memory. You must observe that when the flower becomes visible by the refraction of the ray, you do not see it in the situation which it really occupies, but the image of the flower appears higher in the cup; for as objects always appear to be situated in the direction of the rays which enter the eye, the flower will be seen at B, in the direction of the refracted ray.

_Emily._ Then, when we see the bottom of a clear stream of water, the rays which it reflects, being refracted in their passage from the water into the air, will make the bottom appear higher than it really is.

_Mrs. B._ And the water will consequently appear more shallow. Accidents have frequently been occasioned by this circumstance; and boys, who are in the habit of bathing, should be cautioned not to trust to the apparent shallowness of water, as it will always prove deeper than it appears.

The refraction of light prevents our seeing the heavenly bodies in their real situation: the light they send to us being refracted in passing into the atmosphere, we see the sun and stars in the direction of the refracted ray; as described in fig. 4, plate 19., the dotted line represents the extent of the atmosphere, above a portion of the earth, E B E: a ray of light coming from the sun S, falls obliquely on it, at A, and is refracted to B; then, since we see the object in the direction of the refracted ray, a spectator at B, will see an image of the sun at C, instead of its real situation, at S.

_Emily._ But if the sun were immediately over our heads, its rays, falling perpendicularly on the atmosphere, would not be refracted, and we should then see the real sun, in its true situation.

_Mrs. B._ You must recollect that the sun, is vertical only to the inhabitants of the torrid zone; its rays, therefore, are always refracted, in this latitude. There is also another obstacle to our seeing the heavenly bodies in their real situations: light, though it moves with extreme velocity, is about eight minutes and a quarter, in its passage from the sun to the earth; therefore, when the rays reach us, the sun must have quitted the spot he occupied on their departure; yet we see him in the direction of those rays, and consequently in a situation which he had abandoned eight minutes and a quarter, before.

_Emily._ When you speak of the sun's motion, you mean, I suppose, his apparent motion, produced by the diurnal motion of the earth?

_Mrs. B._ Certainly; the effect being the same, whether it is our earth, or the heavenly bodies, which move: it is more easy to represent things as they appear to be, than as they really are.

_Caroline._ During the morning, then, when the sun is rising towards the meridian, we must (from the length of time the light is in reaching us) see an image of the sun below that spot which it really occupies.

_Emily._ But the refraction of the atmosphere, counteracting this effect, we may, perhaps, between the two, see the sun in its real situation.

_Caroline._ And in the afternoon, when the sun is sinking in the west, refraction, and the length of time which the light is in reaching the earth, will conspire to render the image of the sun, higher than it really is.

_Mrs. B._ The refraction of the sun's rays, by the atmosphere, prolongs our days, as it occasions our seeing an image of the sun, both before he rises, and after he sets; when below our horizon, he still shines upon the atmosphere, and his rays are thence refracted to the earth: so likewise we see an image of the sun, previously to his rising, the rays that fall upon the atmosphere being refracted to the earth.

_Caroline._ On the other hand, we must recollect that light is eight minutes and a quarter on its journey; so that, by the time it reaches the earth, the sun may, perhaps, have risen above the horizon.

_Emily._ Pray, do not glass windows, refract the light?

_Mrs. B._ They do; but this refraction would not be perceptible, were the surfaces of the glass, perfectly flat and parallel, because, in passing through a pane of glass, the rays suffer two refractions, which, being in contrary directions, produce nearly the same effect as if no refraction had taken place.

_Emily._ I do not understand that.

_Mrs. B:_ Fig. 5, plate 19, will make it clear to you: A A represents a thick pane of glass, seen edgeways. When the ray B approaches the glass, at C, it is refracted by it; and instead of continuing its course in the same direction, as the dotted line describes, it passes through the pane, to D; at that point returning into the air, it is again refracted by the glass, but in a contrary direction to the first refraction, and in consequence proceeds to E. Now you must observe that the ray B C and the ray D E being parallel, the light does not appear to have suffered any refraction: the apparent, differing so little from the true place of any object, when seen through glass of ordinary thickness.

_Emily._ So that the effect which takes place on the ray entering the glass, is undone on its quitting it. Or, to express myself more scientifically, when a ray of light passes from one medium into another, and through that into the first again, the two refractions being equal, and in opposite directions, no sensible effect is produced.