Visual angle

“ To be satisfactorily seen as a single composition or group they ought to lie, all of them, within a visual angle of thirty degrees. We may, within these limits, disregard [Pg 23] the fact that visual attractions lose their force as they are removed from the center of the field of vision. As equal attractions in the field of vision, the dots in any unsymmetrical arrangement may be brought into a balance by weighing the several attractions and indicating what I might call the center of equilibrium. This is best done by means of a symmetrical inclosure or frame. ”

“ When it is intended that the pictures taken are to be viewed by an instrument that requires their distance from the eyes to be less than the focal length of the lens used in their formation, what is the result? Why, that they subtend an angle larger than in nature, and are consequently apparently increased in bulk; and the obvious remedy is to increase the angle between the points of generation in the exact ratio as that by which the visual distance is to be lessened. ”

“ When light falls on a transparent body, part is reflected and part is refracted. The angle which the ray makes with the normal, or perpendicular, to the surface at the point of contact is known as the angle of incidence, and the angles which the reflected and refracted rays make with the same normal are known respectively as the angle of reflection and refraction. ”

“ At the same time the eye is slowly developing its power of judging distance. But not for several years does visual perception of distance become in any degree accurate. The eye's perception of distance depends in part on the sensations arising from the muscles controlling the eye, probably in part from the adjustment of the lens, and in part from the retinal image. If one tries to look at the tip of his nose he easily feels the muscle strain caused by the required angle of adjustment. ”

“ When we see any object clearly, it is because the rays of light reflected or radiated from it enter the eye and produce a perfect picture of the object upon the retina. But the perfection of the picture depends upon the distance, size, and illumination of the object relatively to the powers and condition of the eye. The distance determines the angle at which the rays enter the eye. Whatever this angle, the rays must converge upon the retina, or the picture will be defective. ”

“ A very simple geometrical construction, and one which we recommend our young readers to carry out as an exercise in optics, by the simple application of the principle that the angle of incidence is equal to the angle of reflection, allows us to see that the image of any point whatever placed in the center of this triangle of glass plates will be reproduced indefinitely by groups of six images distributed symmetrically around points regularly spaced in the prolongations of the planes of the three glasses. ”

“ What chiefly concerns us here is the fact that the pictures on our retinas are flat, of two dimensions, the same as the canvas on which we paint. If you examine these visual pictures without any prejudice, as one may with a camera obscura, you will see that they are composed of masses of colour in infinite variety and complexity, of different shapes and gradations, and with many varieties of edges; giving to the eye the illusion of nature with actual depths and distances, although one knows all the time that it is a flat table on which one is looking. ”

“ Without much semi-scientific pedantry, the whole science may be understood by balancing a half-crown on the top of the forefinger of your right hand. Hold it up so that its broad plane is parallel to the eye’s plane; put it nearer or further, and it seems to increase or diminish in size. Turn it obliquely, and it appears an oval; put the edge on a line with the eye, and it appears a mere thin straight line. A sphere is the only geometric form that undergoes no perspective changes. The eye is able to take in any given space set at an angle of under sixty degrees. ”

“ Instead of fixing my eye immovably upon one point, I deliberately run it over the leading lines of the view, and then trace lines upon the paper that produce the same effect upon my eye as those in Nature have done. My sketch will at best be imperfect, but its accuracy will be in proportion to the care with which I have examined the outlines in the landscape. In observing an object, we do not then look fixedly at it—we run the eye over it. Let us see what this means.
The retina is not in all parts equally sensitive to light, and the whole of a visual image is not distinctly perceived at once. ”

“ A space that is arched looks wider than it actually is, for the eye unconsciously follows the lines of the arch, and a distance or width effect is the result. The same space treated with a straight line is quickly bridged. The same space treated with lines that come to an angle looks narrower, for the reason that the eye becomes focused by the apex of the angle, and a height effect, not a breadth effect, is the result. ”

“ By looking above a light, or a letter, and then trying to see it as well as when directly regarded, one can produce an illusion of several lights, or letters, arranged vertically. If the strain is great enough, there may be as many as a dozen of them. By looking to the side of the light or letter, or looking away obliquely at any angle, the images can be made to arrange themselves horizontally, or obliquely at any angle. ”

“ When the object, by moving, changes its relations to the eye, the sensation excited by its image even on the same retinal region becomes so fluctuating that we end by ascribing no absolute import whatever to the retinal space-feeling which at any moment we may receive. So complete does this overlooking of retinal magnitude become that it is next to impossible to compare the visual magnitudes of objects at different distances without making the experiment of superposition. ”

“ IV Perspective of a Point, Visual Rays, &c.
We perceive objects by means of the visual rays, which are imaginary straight lines drawn from the eye to the various points of the thing we are looking at. As those rays proceed from the pupil of the eye, which is a circular opening, they form themselves into a cone called the Optic Cone, the base of which increases in proportion to its distance from the eye, so that the larger the view which we wish to take in, the farther must we be removed from it. ”

“ If the eye is elevated above A, say to B, it is plain that the angles EBC and EBD are greater than right angles, or in other words, that the observer sees more than a semi-circle of sky. Hence all measurements made by the sextant are too large. In other words, the elevation of the eye makes the angle too great and therefore the correction for dip is always subtracted. ”

“ In a real view our eyes are directed successively at every object, which we then see clearly and with distinct outlines, everything else—nearer and farther—being indistinct; but being able to change the focal angle of our two eyes and their angle of direction with great rapidity, we are enabled to glance rapidly at each object in succession and thus obtain a general and detailed view of the whole. ”

“ Whether or not, in the case of the retina, our appreciation of the coin’s roundness comes from some unconscious counting process is a problem for the specialist to decide; but at all events, when we consider that the retina and the eye are Euclidean bodies just like our rulers, the concordance between our computations of shape and size, as determined by rods, and our direct visual appreciation of shape does not appear to present much of a mystery. ”

“ Hence we conclude in general, that when an object is placed at any distance before two mirrors inclined at an angle, which is an even aliquot part of 360°, the symmetry of the picture is perfect, when the eye, considered as a mathematical point, is placed at E, and that the deviation from symmetry increases as the eye recedes from E towards ε. ”

“ Hence it follows that all pictures should be viewed under the same angle of apparent magnitude under which they were seen by the artist as taken photographically, for if we view them at a greater or less angle than this we do not see the same picture as when we looked at the original landscape or portrait, under the same angle of apparent magnitude. ”

“ The mere size of the apparent field of view depends upon obtaining the oblique pencils of light emerging from it to cross the axis at the great possible angle, and to this end the presence of a field-lens is indispensable, which is separated from the eye-lens by a considerable interval. ”

“ In the ordinary and natural use of our eyes, we can direct their axes to a fixed star; in this case they must be parallel: we can direct them also to an object six inches distant from the eye; and in this case the axes must make an angle of fifteen or twenty degrees. We see young people in their frolics learn to squint, making their eyes either converge or diverge, when they will, to a very considerable degree. Why should it be more difficult for a squinting person to learn to look straight when he pleases? ”

“ The great sweep of vision, a sweep covering a hundred subjects perhaps, is obtained by turning the eyes up or down or sideways. But to be true—that is, to see one picture at a time—the eye should be fixed like the lens of a camera, the limit of the picture being the range of the eye and no more. A departure from this rule not only confuses your perspective but crowds a number of points of interest into the square of your canvas, when there is really only one centre point before you in nature ”

“ The eye moves through a series of angles toward the angle which contains the greatest number of attractions. The reader can hardly fail to feel the successive axes of symmetry as a retarding element in this Rhythm.
46. Sixth. Symmetrical relations of position may be repeated in progressions of scale and of intervals. In that case we get two movements, one caused by a gradual increase in the number of attractions in successive angles of vision, the other being due to a gradual crowding together and convergence of attractions in the same series of angles. ”

“ This happens, because the shape of small objects, at an equal distance, comes to the eye under a more acute angle than the large ones, and the perception of them is less, in proportion as they are less in magnitude. It follows then, that if the large objects, by being removed to a great distance, and consequently coming to the eye by a small angle, are almost lost to the sight, the small objects will entirely disappear. ”

“ But there is great diversity of opinion as to the extent of the angles requisite for producing the precise stereoscopic or distantial effect of nature. For myself I prefer Professor Wheatstone's rule, 1 in 25 for objects beyond 50 feet distant. For portraits I find the best angle 1 in 10 when the sitter is 10 feet off, and for busts about 1 in 5 when placed about 5 or 6 feet from the cameras. ”

“ The angle formed between any objects and our eye is the only means by which our sight estimates their size and distance, and as this angle is the simple effect of complex causes, the judgment we form does not distinguish between the several causes; we are compelled to be inaccurate. ”

“ Thus we see that an image is formed on both eyes, and we consequently see the object, whatever it may be, repeated twice. By degrees, however, the eyes gain the power of converging their axes on objects at different distances, so that they fall on similar portions of each retina, and so convey a single impression to the brain. ”

“ If, therefore, the cut has dimensions, the cut will have and the whole of visual space .
If all the red sensations affecting the same point of the retina were regarded as identical, the cut reducing to a single element would have 0 dimension, and visual space would have 2.
And yet most often it is said that the eye gives us the sense of a third dimension, and enables us in a certain measure to recognize the distance of objects. ”

“ The normal focus is for distant objects. When we read a book the eye adapts itself to the work. The ligaments relax and the lens decreases in diameter while thickening at the centre, until its curvature is such as to focus all rays from the book sharply on the retina. If we suddenly look through the window at something outside, the ligaments pull on the lens envelope and flatten the curves.
This wonderful lens is achromatic, and free from spherical aberration and distortion of image. ”

“ The only reminder of the top view is the eye or point of vision, the picture plane that falls together for the sake of convenience with the horizon of the end view and the ray that determines the measurement point M, which is, in this suppressed reproduction, absolutely necessary, in order to find the apparent position of the real corners behind the picture plane. ”

“ Perhaps the most important of the images which come in to give depth, volume, solidity to the partly imagined and partly perceived ‘picture-space’ are those which are relicts of eye movements, kinæsthetic images of the convergence of the eyes and accommodation of the lenses according to the distance of the object contemplated. When, as it seems, we look past an object in a picture to some more distant object, seeming in so doing to change the focus of our eyes, we do not as a rule actually make any change. ”

“ The arresting power of the right angle exists at each corner of a rectangular picture, where the 160vertical sides meet the horizontal base, and this presents a difficulty, because you do not wish the spectator's attention drawn to the corners, and this dramatic combination of lines always attracts the eye. A favourite way of getting rid of this is to fill them with some dark mass, or with lines swinging round and carrying the eye past them, so that the attention is continually swung to the centre of the picture. ”