Fig III
Fig IV
Fig V
We cannot admit that the salmon sees the fly against the bright light of the sky. This does happen at times, but such moments are the exception, not the rule. If the salmon saw the fly against the background of bright sky, the fly would undoubtedly appear black, a dark silhouette on a white ground. In that case it might well be argued that as the fish sees no colour, colour perception, being useless to the fish, is not one of its possessions. But the refraction of the light, owing to the density of the water, entirely alters the case. When a ray of light enters a body of greater density it becomes bent, and the bending always takes place in the dense body towards a line drawn perpendicular to the surface at the point of contact. This bending of the light follows a fixed law. In whatever direction the light strikes the body the sine of the angle of incidence is to the sine of the angle of refraction in a constant ratio. In the refraction from air to water the ratio is very nearly four to three. To explain more fully (see fig. I), a ray of light AC strikes the water at C and is refracted to B. With the centre C describe a circle, cutting the ray of light at A and B, and from these points draw lines perpendicular to the surface of the water AF and BG. The distance CF is to the distance CG as 4 to 3. If CF be 4 ft. then CG is 3 ft. Again, suppose the ray of light comes from a point say, near the surface (see fig. 2), then CF will be almost equal to the radius of the circle. But if CF is 4 ft. then CG is 3 ft., therefore the point G must be a foot from D, however small the angle the ray of light makes with the surface of the water at C. The converse holds true. A ray of light from B will be refracted to A; but if the ray comes from H it will not be able to get out at C, and will be reflected to K. One can always see into a dense body, but it is not always possible to see out. The angle at which one ceases to see out of a dense medium is called the critical angle. Therefore, if a fish in the water looks towards the surface so that its line of vision makes an angle with the surface somewhat less than 45°, say 42°, the fish cannot see out (see fig. 3). Now, if we take into account that when light strikes water at a very small angle with the surface a large part is reflected and, comparatively speaking, very little refracted to the fish’s eye, a fairly reasonable angle for a fish to see out of the water at is 45° or more. What follows? If our salmon is at a depth of 4 ft., then if right above its eye we describe a circle (see fig. 4) 4 ft. in radius, within this circle lie the only points in the whole river from which it is possible for the fish to see the sky. Where does the fish see the banks of the river? The line in which light enters the eye is that in which the object is seen. The banks B will be seen as if at B. All the landscape and sky will be seen within the circle, that is, within the cone whose apex is the fish’s eye, and base the circle on the surface. It may not be out of place to point out that a fish at some distance from the bank in a quiet pool may be seen distinctly by an observer, while the fish may not be able to discern him. The man on the bank sees the fish lit by all the light of the sky above and reflected to his eye. The fish, on the other hand, sees the observer only by the light reflected by his body, much of which light never reaches the fish’s eye at all, being reflected at the surface of the water. Referring to fig. 3, if the fish look at a point X outside the magic circle, it will not see out of the water. The surface acts as a reflector and all the fish can see in this direction is a picture of the bed of the river at Y. We are not considering the point whether a fish can see an object in the water at X, but whether the fish can see the sky there; all the sky that the fish can see is within the circle already mentioned. We have remarked that the fish cannot, while in its normal position, see directly above its head, therefore even in part of this circle the sky will be invisible. Suppose an object is only 3 ft. above the fish, then the area in which the fish can see it against the sky will be a circle only 6 ft. in diameter. It is only when anything drifts within the cone already described that the fish can see it against the sky. This may be illustrated in the following striking manner. Take a glass globe (see fig. 5) and fill it exactly half full of water, paint the part filled by the water any dark colour, leaving a small clear space at AB and Y. Now, if a ray XC falls on the centre C it will be refracted to Y, and then come out into the air without further refraction. If we look through Y towards C we are in the position of the fish in the water. This is true for a small pencil of light. If, however, we look towards C through the opening A, we see out of the whole surface, and can see an object above the surface. If we look from B towards C, our line of vision makes an angle of less than 45° with the surface and we cannot see out of the surface, for it then becomes a mirror and reflects the painted side of the vessel and nothing more. Drop a fly at C, and from B you will not see the fly till it actually enters the water, and you will see only that part of it which is immersed in the water, together with its reflection. The photograph (fig. 6) shows what happens.
Fig. VI.