Part Two Chapter ThreeThe Camera Obscura
1. Introduction 2. Astronomical Context 3. Inversion of Images 4. Non-interference 5. Images all in all 6. Intensity of Light and Shade or Image 7. Contrary Motion 8. Size of Aperture 9. Shape of Aperture 10. Number of Apertures 11. Apertures and Interposed Bodies 12. Spectrum of Boundaries 13. Camera Obscuras and the Eye 14.Conclusions
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Figs. 678-679:Pinhole apertures and camera obscuras in observations of the sun on Triv 6v and A20v.
- Introduction
Leonardo has commonly been credited with the invention of the camera obscura.1. This is not true. Unequivocal descriptions of the instrument go back at least until the ninth century A.D. 2 and by the thirteenth century it had assumed an important function in astronomy.3 On the fourth of June, 1285, for instance, William of St. Cloud used a camera obscura to observe an eclipse of the sun.4 This use of the camera obscura develops in the fourteenth century and in the latter fifteenth century provides one source of Leonardo's interest in the instrument. He uses it, for example, to estimate the size and distance of the sun and moon.
The aperture of the camera obscura is, for Leonardo, analogous to the aperture of the pupil and this leads him to study various characteristics of apertures: how images passing through them are inverted, how they do not interfere with one another, how such images are "all in all and all in every part"; how they can vary their intensity, and how they move in a contrary direction beyond the aperture.
He considers the effect of changing the size of the aperture and examines in some detail both the properties of a single aperture with a changing number of sides and the characteristics of multiple pinhole images. From a note on CA277va (1513-1514) cited above (see p. ), he clearly intended to adopt these findings for two additional books on light and shade. Indeed many of the experiments that he had made with umbrous bodies in the open he repeats in combination with a camera obscura, now focussing on a particular phenomenon: how the boundaries between light and shade are actually a series of subtle graduations. These late studies of 1508-1510, as will be shown, have important consequences for his theories of vision and perception. But before considering these, we need to examine the details of his camera obscura studies.
- Astronomical Context
Leonardo's earliest extant reference to the use of an aperture in observing eclipses is on Triv.6v (fig. 678, 1487-1490):
Way of seeing the sun eclipsed without hurting the eye. Take a card and make the aperture with a needle and through these /pinhole/ apertures look at the sun.
In this case the image is seen directly and the aperture serves merely to screen off excessive light. On CA270vb (c. 1490) he describes a case where the image is seen indirectly under the heading:
How bodies...send...their form and heat and power beyond themselves.
When the sun, through eclipses, remains in the form of the moon, take a thin sheet of iron
and in this make a little hole and turn the face of this sheet towards the sun...holding a piece
of cardboard a 1/2 braccia behind this and you will see the similitudes of the sun come in a
lunar shape, similar to its shape and colour.
Immediately following he offers a (cf. fig. 679).
Second example.
This said sheet /of iron/ will also do the same at night with the body of the moon and also with the stars. But from the sheet /of iron/ to the cardboard there is by no means to be any other aperture other than this little hole and this is similar to a square box, of which the faces above and below and the two on the side of the card are of solid wood; that in front has the sheet /of iron/ and that behind, a thin white cardboard or paper pasted to the edges of the wood.
Finally he provides an illustration that simulates the effects produced by these natural phenomena:
Third example.
Again take a candle of wax, which makes a long light and placed in front of this aperture, the said light will appear on the paper opposite in a long form and similar to the form of its cause, but upside down.
This example, described on CA270vb, is illustrated in diagrams on CA126ra (fig. 156), CA125vb (fig. 694), and CU789 (fig. 704). The case of the moon is also considered on A64v (1492):
Because all the effects of luminous bodies are demonstrative of their causes, the moon in
the form of a boat, having passed through the aperture, will produce at the object /i.e. the
wall/ a boat shape.
On A61v (1492) he pursues this theme, now adding an illustration (fig. ):
That perforation of round quality which is half closed will appear in the form of ab and the
part c will be the light and n will be the closed off part and this same happens to the
luminous half-moon.
The problem of the moon's shape continues to perplex him. On CA243ra (1510-1515) he notes:
Since over a long distance a long luminous source makes itself round to us and /yet/ the
horns of the moon do not observe this rule and even the light from nearby observes the
demonstration of its point.
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Figs. 680-681:Use of camera obscura for astronomy on A21r (1492) and by Mario Bettini (1642).
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Figs. 682-683:Uses of camera obscura for astronomy on BM174v and CA243rb.
The use of the camera obscura in determining the diameter of the sun had been discussed by late mediaeval authors such as Levi ben Gerson5 (c.1370). This also interests Leonardo as is shown by a diagram on A20v (fig. 679, cf. A21r, fig. 680 and Mario BEttini, fig. 681) beneath which he adds:
Way of knowing how large the sun is. Make that from a /to/ b there are hundred braccia
and make that the aperture where the solar rays pass is 1/16 of a braccia and note how much
the ray has expanded in percussion.
The problem is not forgotten. On CA225rb (1497-1500) he reminds himself in passing of "the measurement of the sun promised me by Master Giovanni the Frenchman." On BM174v (1500-1505) Leonardo describes a more complex procedure involving a combination of camera obscura and mirror (fig. 682):
ab is the aperture through which the sun passes. And if you could measure the size of the
solar rays at nm, you could see very well the true lines of the concourse of these solar rays,
the mirror standing in ab, and then make the rays reflected at equal angles towards nm. But
in order that you do not then distort (torse) it at nm, take it inside the aperture at cd, which can be measured in the percussion of the solar ray, and then place your mirror at the distance ab and there make fall the rays db /and/ ca and then rebound under equal angles towards cd. And this is the true method: but you need to operate such a mirror at exactly the same month, day and hour and you will do it better than at any other time because in such a distance of the sun, such a pyramid is caused.
The precise function of this procedure is not explained. On Leicester 1r (1506-1509) he alludes to but again does not elaborate on a
Record of how I at first demonstrated the distance of the sun from the earth and with one of its rays which have passed through an aperture in a dark place find its true quantity again and besides this, through the centre of the water to find the size of the earth.
To this problem of sizes and distances of the planets he returns on CA243rb (1510-1515) now providing a more detailed explanation:
If you have the distance of a body you will have the size of the visual pyramid which you will cut near the eye on the window (pariete) and then you remove the eye to that extent, such that the intersection is doubled, and note the space from the first to the 2nd intersection and say: if in so much...space the diameter of the moon increases so much above the first intersection, what will it do in all the space that there is from the eye to the moon? This will make the true diameter of this moon.
The method here described is identical to the surveying procedure used to demonstrate principles of linear perspective on CA42rc, (cf. vol. 1, fig. 122). On CA151va (1500-1506) he gives an alternative method of measuring the distance of the sun, this time using a staff again familiar from the surveying tradition. Lower down on CA243rb he draws a rough sketch of a camera obscura (fig. 683) beneath which he notes "Measure of the size of the sun, knowing the distance." On CA297va (1497-1500) he drafts a passage concerning the use of apertures in a meteorological context:
The solar rays, penetrating the apertures...which are interposed between the various...globosities of clouds, illuminate with their straightness all...the passage interposed...between the earth and this aperture...and tinge from themselves all the sites where they intersect.
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Figs. 684-685:Apertures in clouds and camera obscuras on CU476 and CA248va.
This he drafts again directly below:
The solar rays penetrating the apertures interposed between the various globosities of clouds...make a straight and spreading course towards the earth where they are intersected...illuminating...with their...brightness all the penetrated air.
These drafts serve in turn as the basis for a passage on CU476 (fig. 684, TPL447, 1510-1515):
On the solar rays that penetrate the apertures of clouds.
The solar rays penetrating the apertures positioned between the various densities and globosities of clouds illuminate all the sites where they intersect and even illuminate the darknesses or tinge with themselves all the dark places that are behind them, which darknesses show themselves to be between the intervals of these solar rays.
Also in this late period, on CA248va (fig. 685, 1510-1515), he again mentions the relative intensity of the sun's illuminating in a camera obscura:
ab is brighter than cd. But the point t being illuminated by the narrow aperture by the part of the sun o will be that much less illuminated than being illuminated by the diameter ab to the extent that this o is less than this diameter ab.
These astronomical and meteorological uses of the camera obscura constitute but a small part of Leonardo's concern for this instrument. He is fascinated by the analogies that it offers with the pupil (see below pp. ) and therefore employs the camera obscura to demonstrate such optical principles as inversion of images, their non-interference, and their existence "all in all and all in every part." We shall examine each of these in turn.
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Figs. 686-687:Use of a camera obscura to demonstrate the inversion of images on W19147v (K/P 22v): fig. 688, another example on C6r.
- Inversion of Images
Leonardo believes that images are inverted in passing through the aperture of the pupil. As early as 1489-1490 he employs a camera obscura to demonstrate this principle in a passage on W19147v (K/P 22v):
But if the plane of this interruption has in it a small aperture which enters into a dark home /that is/ dark not by colour but through privation of light, you will see the lines enter through this said aperture /and/ carry on the second wall the entire form of its origin, both with respect to colour and form. But everything will be upside down....
A specific example follows (fig. 686):
Let ab be the origin of the lines. Let de be the first wall; let c be the aperture where the intersection of the lines is. Let fg be the last wall. On the last wall and percussion you will find that a remains below at the place g and g below rises above to the place f.
He pursues this eye-camera obscura analogy on C6r (fig. 688, 1490-1491):
All the things that the eye sees beyond little apertures are seen upside down by this eye and are known as right side up.
Let ad be the pupil (luce) that sees through the aperture n. The line eh is seen by the lower part of the eye; dh is seen by the upper part of the pupil.
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Figs. 689-696:Demonstrations of inversion in camera obscuras. Fig. 689, Forst. III 29v; figs. 690-691, CA373rb; fig. 692, CA155rde; fig. 693, BM170v; fig. 694, CA125vb; figs. 695-696, CA345vb.
He illustrates this inversion principle in sketches without text on Forst III 29v (fig. 869, 1490-1493), CA155rde (fig. 692, 1495-1497) and BM170v (fig. 692, 1492); then mentions it again on BM232v (1490-1495): “The bases of inverted pyramids, if they are in a dark place, will show upside down the shape and cause of their source.” A further illustration occurs on CA125vb (fig. 694, 1492) accompanying which he drafts an explanation:
The sun and every luminous body, which sends its rays through an aperture smaller than it in size, will send the rays upside down behind this aperture and you will see the experience with a lighted candle, taking its rays beyond an aperture smaller than it.
On CA126ra (c. 1492) the problem is further illustrated (fig. 156). Thereafter, more than a decade passes before he broaches the problem again on CA345vb (figs. 695-696, 1505-1508):
And they /the images/ impress themselves on the wall opposite the said point, perforated in a thin wall, and for this reason the eastern part will impress itself in the western part of such a wall and the western in the eastern and likewise the northern in the southern and conversely, etc.
In the Manuscript D he discusses the problem of inversion at length. A first passage on D10r (c. 1508) is entitle:
Of the species of objects that pass through narrow apertures into a dark place.
It is impossible that the species of bodies that penetrate through apertures into a dark place do not reverse themselves. This is proved by the 3rd of this which states (the particles of each umbrous ray are always rectilinear).
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Figs. 697-698:Demonstrations concerning inversion of images on D10r and D8r.
To demonstrate this he provides a concrete example (fig. 697):
Therefore the part b of the object ab, passing through the aperture n into the dark place oqpr, will impress itself on the wall pr on the site c and the opposite extremity a of the same object ab will impress itself on the wall cr /sic: pr/ at the point r /sic:c/ and thus the right extremity of such an object makes itself left and the elft makes itself right, etc.
On D8r he pursues this analogy between eye and camera obscura under the heading:
How the species of objects received by the eye intersect inside the albugineous humour.
The experience which shows that objects send their intersected species or similitudes inside the eye in the albugineous humour is shown when the species of illuminated objects pass through some small round aperture into a habitation that is very dark, then you will receive such species on a white piece of paper...placed in such a habitation somewhat near this aperture and you will see all the aforesaid objects on this paper with their proper shapes and colours but they will be smaller and inverted as a result of the said intersection. Which images if they originate in the eye illuminated by the sun appear properly depicted on this paper which would be very thin and seen from behind.
A concrete demonstration follows (fig. 698):
And let the said aperture be made in a very thin sheet of iron. Let a, b, c, d /and/ e be the said objects illuminated by the sun. Let or be the face of the dark habitation in which is the said aperture nm. Let st be this /piece of paper where the rays of the species of these objects are intersected upside down, /and/ because their rays are straight a /on the/ right makes itself left at k and e /on the/ left makes itself on the right at f and it does the same inside the pupil.
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He again mentions this way in which images are inverted in passing on W19150v (K/P 118v(a), fig. 699, 1508-1510): "No image of however small a body penetrates the eye without being turned upside down....." On CA241vc (also 1508-1510) he produces two further drafts:
Every umbrous and luminous species which penetrates through the apertures...behind such a penetration turns (upside down after such a penetration) in contrary aspects all the parts of its size.
Every umbrous and luminous species interests after the penetration made behind the apertures, turning in contrary aspect every part of their size.
These he crosses out and reformulates:
The rays of umbrous and luminous species intersecting after the penetration made by them inside the apertures, turn in contrary aspect every part of their size.
4.NON-INTERFERENCE
The non-interference of images is another phenomenon which he demonstrates using the camera obscura. On A93r (BN2038 13r, 1492), for instance, he shows how a red, white and yellow light can intersect without interference (fig. 700). Similar demonstrations occur on CA256rc (figs. 701-702, c.1492) involving a red, green and yellow light and a red, white and green light. Accompanying these are a series of draft notes concerning the intensity of colour, light and shade passing through apertures:
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Figs. 700-702:Demonstrations concerning non-interference of images. Fig. 700, A93r; figs. 701-702, CA256rc.
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Figs. 703-705:Further demonstrations concerning non-interference of colours in a camera obscura on K/P 118r, CU789, K/P 118v.
That colour which is more illuminated will show itself better in the percussion made by its rays within the aperture.