كتاب المناظر (The Optics of Ibn al-Haytham, Books I-III)

I 9b

therefore shows that the distances from which a visible object can be perceived and the distances at which it disappears depend on the size of the object.

I 10a

[14] Furthermore, we find that the distances from which sight can perceive visible objects vary with the lights existing in these objects: a more intensely illuminated object may be perceived by sight from a distance at which objects of equal size are invisible—given that the lights in these objects are fainter than the light of that object. For let a fire at some place be surrounded by objects or bodies each of which is equal in size to the bulk of the fire (or not greatly different from it) and illuminated by the light of that fire. A man approaching the fire from a considerable distance in a dark night will see the fire before he sees any of the objects or bodies surrounding it, although they are equal to or greater than the fire and are illuminated by its light. When that man approaches the fire there will appear to him the objects round the fire and close to it. Those objects nearer the fire and of strong light will appear before those which are farther from it and of faint light. Then, when he reaches the fire, there will appear to him all the visible objects round and near it. Similarly, when we experimentally examine distant visible objects in daylight we find that those illuminated by sunlight or by strong lights appear from distances at which there disappear the objects of equal size and colour when they are in the shadow or illuminated by faint light.

[15] It follows from this that the distances from which sight can perceive visible objects and the distances at which they become invisible vary with the lights existing in those objects.

I 10b

[16] We also find that brilliant-white and bright-coloured bodies are visible from distances at which dull, earthy and dark bodies 1: These are objects lacking reflective surface or luminosity. disappear from view, even when the bodies are identical in size and light and all other conditions except colour. Thus when ships are sailing at a great distance in the sea, their sails, if white, look like stars from the distance; sight perceives their whiteness but not the ships themselves nor anything in them that is not brilliant white as long as they are far distant. Then, when the ships approach the eye they and their contents become visible, even though sight was not previously able to perceive them when it perceived only their sails.

I 11a

[17] It is similarly the case with objects on the surface of the ground when they are of equal (or not very different) size and of different colours (some being brilliant white, others of bright colours and yet others of earthy or dull colours) 1: The author refers here to matte or non-reflective pigments. and all are illuminated by the same light: if someone approaches them from a considerable distance he will see the brilliant white objects before any of the others; when he comes nearer, the bright-coloured objects will appear before those of the earthy or dull colours; then as he comes nearer still, the others will become visible, until they are all apparent.

[18] It follows from this that the distances from which objects can be seen and the distances at which they cease to be visible are according to the objects' colour.

[19] We also find that the distances from which an object can be seen, and the distances at which it ceases to be visible, are according to the power of sight. For a man of keen sight may perceive an object from a distance at which that same object would not be visible under the same conditions to a man of weak sight.

[20] It follows from what we have stated and gathered by induction regarding distances that the distances from which an object can be perceived and those at which an object becomes invisible are according to the conditions and properties of the object itself, and also according to the strength or weakness of the sight itself that perceives it.

I 11b

I 12a

[21] Therefore, from all that we have stated and found by induction and experiment to be uniform and subject to no variation or contradiction, it is evident that sight does not perceive any object that exists with it in the same air and is not perceived by reflection, unless that object combines the conditions we have stated—namely: that there exists between it and the eye a certain distance proportionate to that object; that it lies opposite the eye—I mean that an imaginary line exists between each point on its visible surface and a certain point on the surface of the eye; that light exists in it, whether from itself or from another object; that it is of a certain size in relation to the sensitive power of the eye; that the air or body between it and the surface of the eye is of a continuous transparency uninterrupted by any opaque body; that it is opaque, or of some opacity—I mean that it is either non-transparent or its transparency is denser than that of the air or of the transparent body extending between it and the surface of the eye—[it being understood that] an opaque body must possess colour or something like colour 1: Ibn al-Haytham argues that colour is a fundamental property of visible opaque surfaces., and the same is true of a transparent body with some density in it. These, then, are the conditions which must combine in a visible object for vision to be effected. When these conditions combine in an object, and sight is free from defects, it will perceive that object. When sight lacks one of these conditions, it will not perceive the object in respect of which that condition is lacking. That being so, these conditions are therefore the characteristic properties of sight without the concurrence of which vision cannot be accomplished.

I 12b

[22] It is also manifest by induction that if any seen object is moved away from the eye to the limit where it becomes invisible, then between the point at which that object disappears and the surface of the eye there exist many different distances which cannot be enumerated or determined and from each of which the eye truly perceives that object and all of its parts and visible properties. If the eye acquires a true perception of the object at one of these distances, then moves away from it gradually and in orderly manner, those small parts and fine features (if such exist in the object), like designs, 1: Likely referring to patterns or surface engravings. incisions, creases or dots, will disappear before the object disappears as a whole, and the smaller and finer among these features will disappear before those that are larger and more gross. The distances at which the small parts become invisible and the fine features confused and indistinct are found to be many, indeterminate and unlimited.