The Notebooks

202. The shadow cast by an object on a plane will be smaller in proportion as that object is lighted by feebler rays. Let _d e_ be the object and _d c_ the plane surface; the number of times that _d e_ will go into _f g_ gives the proportion of light at _f h_ to _d c_. The ray of light will be weaker in proportion to its distance from the hole through which it falls. FIFTH BOOK ON LIGHT AND SHADE. Principles of reflection (203. 204). 203. OF THE WAY IN WHICH THE SHADOWS CAST BY OBJECTS OUGHT TO BE DEFINED. If the object is the mountain here figured, and the light is at the point _a_, I say that from _b d_ and also from _c f_ there will be no light but from reflected rays. And this results from the fact that rays of light can only act in straight lines; and the same is the case with the secondary or reflected rays. 204. The edges of the derived shadow are defined by the hues of the illuminated objects surrounding the luminous body which produces the shadow. On reverberation. 205. OF REVERBERATION. Reverberation is caused by bodies of a bright nature with a flat and semi opaque surface which, when the light strikes upon them, throw it back again, like the rebound of a ball, to the former object. WHERE THERE CAN BE NO REFLECTED LIGHTS. All dense bodies have their surfaces occupied by various degrees of light and shade. The lights are of two kinds, one called original, the other borrowed. Original light is that which is inherent in the flame of fire or the light of the sun or of the atmosphere. Borrowed light will be reflected light; but to return to the promised definition: I say that this luminous reverberation is not produced by those portions of a body which are turned towards darkened objects, such as shaded spots, fields with grass of various height, woods whether green or bare; in which, though that side of each branch which is turned towards the original light has a share of that light, nevertheless the shadows cast by each branch separately are so numerous, as well as those cast by one branch on the others, that finally so much shadow is the result that the light counts for nothing. Hence objects of this kind cannot throw any reflected light on opposite objects. Reflection on water (206. 207). 206. PERSPECTIVE. The shadow or object mirrored in water in motion, that is to say in small wavelets, will always be larger than the external object producing it. 207. It is impossible that an object mirrored on water should correspond in form to the object mirrored, since the centre of the eye is above the surface of the water. This is made plain in the figure here given, which demonstrates that the eye sees the surface _a b_, and cannot see it at _l f_, and at _r t_; it sees the surface of the image at _r t_, and does not see it in the real object _c d_. Hence it is impossible to see it, as has been said above unless the eye itself is situated on the surface of the water as is shown below [13]. [Footnote: _A_ stands for _ochio_ [eye], _B_ for _aria_ [air], _C_ for _acqua_ [water], _D_ for _cateto_ [cathetus].--In the original MS. the second diagram is placed below line 13.] Experiments with the mirror (208-210). 208. THE MIRROR. If the illuminated object is of the same size as the luminous body and as that in which the light is reflected, the amount of the reflected light will bear the same proportion to the intermediate light as this second light will bear to the first, if both bodies are smooth and white. 209. Describe how it is that no object has its limitation in the mirror but in the eye which sees it in the mirror. For if you look at your face in the mirror, the part resembles the whole in as much as the part is everywhere in the mirror, and the whole is in every part of the same mirror; and the same is true of the whole image of any object placed opposite to this mirror, &c. 210. No man can see the image of another man in a mirror in its proper place with regard to the objects; because every object falls on [the surface of] the mirror at equal angles. And if the one man, who sees the other in the mirror, is not in a direct line with the image he will not see it in the place where it really falls; and if he gets into the line, he covers the other man and puts himself in the place occupied by his image. Let _n o_ be the mirror, _b_ the eye of your friend and _d_ your own eye. Your friend's eye will appear to you at _a_, and to him it will seem that yours is at _c_, and the intersection of the visual rays will occur at _m_, so that either of you touching _m_ will touch the eye of the other man which shall be open. And if you touch the eye of the other man in the mirror it will seem to him that you are touching your own. Appendix:--On shadows in movement (211. 212). 211. OF THE SHADOW AND ITS MOTION. When two bodies casting shadows, and one in front of the other, are between a window and the wall with some space between them, the shadow of the body which is nearest to the plane of the wall will move if the body nearest to the window is put in transverse motion across the window. To prove this let _a_ and _b_ be two bodies placed between the window _n m_ and the plane surface _o p_ with sufficient space between them as shown by the space _a b_. I say that if the body _a_ is moved towards _s_ the shadow of the body _b_ which is at _c_ will move towards _d_. 212. OF THE MOTION OF SHADOWS. The motion of a shadow is always more rapid than that of the body which produces it if the light is stationary. To prove this let _a_ be the luminous body, and _b_ the body casting the shadow, and _d_ the shadow. Then I say that in the time while the solid body moves from _b_ to _c_, the shadow _d_ will move to _e_; and this proportion in the rapidity of the movements made in the same space of time, is equal to that in the length of the space moved over. Thus, given the proportion of the space moved over by the body _b_ to _c_, to that moved over by the shadow _d_ to _e_, the proportion in the rapidity of their movements will be the same. But if the luminous body is also in movement with a velocity equal to that of the solid body, then the shadow and the body that casts it will move with equal speed. And if the luminous body moves more rapidly than the solid body, the motion of the shadow will be slower than that of the body casting it. But if the luminous body moves more slowly than the solid body, then the shadow will move more rapidly than that body.