Eye disorders > The eye > Eye convergence

Eye convergence


Convergence - -This is the remaining element of distinct binocular vision, and with it accommodation is very intimately linked, so that usually for every increase of the convergence a certain increase in the accommodation takes place.

Convergence is the power of directing the visual axes of the two eyes to a point nearer than infinity, and is brought about by the action of the internal recti muscles.

When the eyes are completely at rest, the optic axes are either parallel, or more usually slightly divergent. The angle thus formed between the visual and the optic axis is called the angle a, and varies according to the refraction of the eye. In emmetropia the angle is usually about 5° in hypermetriopia it is greater,
sometimes about 7° or 8°, giving to the eyes an appearance of divergence; in myopia the angle is less, often about 2°, or the optic axis may even, in extreme cases, fall on the inside of the visual axis, when the angle a is spoken of as negative; so that in myopia there is frequently an appearance of convergence, giving one the idea of a convergent squint; hence the mere look of the patient's eyes with regard to their axes is not always quite reliable.

The object of convergence is the directing of the yellow spot in each eye towards the same point, so as to produce singleness of vision; diplopia, or double vision, at once resulting when the image of an object is formed on parts of the retina which do not exactly
correspond in the two eyes.

To test the power of convergence prisms are held with their bases outwards. The strongest prism which it is possible to overcome, that is, the prism which does not produce diplopia on looking through
it at a distant object, is the measure of the convergence, and varies in different persons, usually between prisms of 20° and 30°, divided between the two eyes. This is the relative convergence for infinity.

In considering convergence, we have not only to bear in mind the condition of the internal rectimuscles, but also the state of equilibrium produced by them and the action of their antagonists, external recti.

The nearer the object looked at, the more we have to converge, and the greater the amount of accommodation brought into play. Hence, on comverging to any particular point, we usually also involuntarily
accommodate for that point, the internal recti and ciliary muscles acting in unison.

Nagel has proposed a very simple and convenient plan, by which we may express the convergence in wares, calling the angle formed by the visual and median lines, as at M', the metrical angle.

In fig. 32 E E' represent the centres of rotation for the two eyes; E H E' is the base line between the eyes. When the eyes are fixed on some distant object, the convergence being passive, the visual lines are parallel or almost so, as E A, E' A'; the angle is then at its minimum, and it is said to be adapted to its punctum remotum; this then, being at infinity, is expressed, C* = ∞ (C is the sign for convergence).

If the eyes be directed to an object one metre away, the metrical angle E M' H equals one, i.e. C = 1. If the object is 50 cm. off then C=2; if 10 cm, then (100/10=10) C=10. If the object had been beyond 1 meter, but not at infinity, say 4 metres, then C = 1/4.

When the visual lines, instead of being parallel, diverge, then the punctum remotum is found by continuing these lines backwards till they meet at c, behind the eye : the convergence is then spoken of
as negative.

When the eyes are directed to the nearest point at which they can see distinctly, say at M''', the angle of convergence is at its maximum, and it is said to be adapted to its punctum proximum.

The distance between the punctum proximum and the punctum remotum is the range of convergence.

The amplitude of convergence is the whole convergence that can be put in force, and we express it by the formula:

c = p - r

The punctum remotum of convergence is seldomly situated at a finite distance ; sometimes it is exactly at infinity, but in the majority of cases it is situated beyond infinity, i.e. the visual lines diverge slightly. In order to measure. this divergence, and so obtain the punctum remotum of convergence, we place before the eyes prisms with their bases inwards (abducting prisms); and the strongest through which the person is still able to see singly is the measure of the negative convergence.

Prisms are numbered in degrees according to the urgle of the prism. The deviation produced by a prism is equal to half its angle; thus prism 8 will produce a deviation of the eye of 4°, and prism 20 a
deviation of 10°.

When a prism is placed before one eye, its action is equally divided between the two eyes.

To take an example: if an abducting prism of 8° placed before one eye (or what is the same thing, 4° before each eye) be found to be the strongest through which a distant object can be seen singly, then each eye in our example has made a movement of divergence, equal to 2°, and the punctum remotum of convergence in this case is therefore negative, and is expressed - 2°.

A good way for finding the punctum remotum of convergence is by Maddox's test, which consists of a small glass rod placed behind a stenopaic slit; when this is held horizontally before the right eye and the flame of the candle viewed from a distance of 6 meters with both eyes open, the left eye receives the image of the flame, while the right receives the image which is drawn out by the rod into a long vertical strip of light; and since the image received by the two eyes is very different there is no tendency to fusion, and the eyes take up-their position of rest. A suitable scale placed behind the candle will give us the amount of convergence or divergence in meter angles, according to the position occupied by the streak of light on the scale. Should the patient be a myope or hypermetrope he should wear his correction when this test is applied.

To find the punctum proximum of convergence, hold a prism, base outwards (adducting prism), before one eye, and the strongest which can be so employed without producing diplopia divided between the two eyes, gives the punctum proximum of convergence in degrees. But the accommodation must be stimulated at the same time by means of concave glass, otherwise we only obtain the relative punctum proximum. This can be reduced to meter angles as before.

Or a simpler plan is to measure it with Landolt's ophthalmo-dynamometer, which is a small instrument consisting of a black metallic cylinder, A, made so as to fit upon a candle, B. The cylinder has a vertical slit .3 mm. in breadth, covered by ground glass: the candle being lighted, this slit forms a luminous line,
FIG. 33.

and will serve as a fixation object. A tape measure is conveniently attached, being graduated in centimetres on one side, and on the other in the corresponding numbers of metre angles.
To find the punctum proximum of convergence, the measure is drawn out to about 70 cm., its case being held beside one of the eyes of the patient, while the object of fixation is placed in the median line. If the illuminated line is seen singly, by pressing the knob
of the case the spring rolls up the tape, and the fixation object is brought nearer the eye. So soon as the patient commences to see double, the nearest point of convergence is obtained, and the maximum of convergence is read off the tape in metre angles. This experiment should be repeated several times.

In a normal case the minimum of convergence is usually abont -1 in a, the maximum 9.5 m a; so that the amplitude of convergence equals 10.5 m a.

We know that the accommodation increases the nearer the object approaches, hence we see that both the convergence and accommodation increase and decrease together; and in recording the convergence in
the manner proposed by Nagel, it will be seen that in the emmetropic eye, the number which expresses the metrical angle of convergence expresses also the state of refraction for the same point. This is a great advantage. Thus when looking at a distant object, the angle of convergence is at infinity C = ∞ ; and the refraction is also at infinity, A = ∞. When the object is at 1. metre the angle of convergence = 1, and the amount of accommodation put into play = 1 D. When the object is at 25 cm., then the angleof convergence = 4, and the amount of accomodation = 4 D.

The amplitude of convergence is somewhat greater than the amplitude of accommodation, passing it both at its punctum remotum and its punctum proximum.

The following table shows the angle of convergence in degrees, for different distances of the object, when the eyes are 6.4 cm. apart :





















Distance of the object from the eyesThe metrical angleValue expressed in degrees
1 meter11°50'
50 cm23°40'
33 cm35°30'
25 cm47°20'
20 cm59°10'
16 cm611°
14 cm712°50'
12 cm814°40'
11 cm916°30'
10 cm1018°20'
9 cm1120°10'
8 cm1222°
7.5 cm1323°50'
7 cm1415°40'
6.5 cm1527°30'
6 cm1629°20'
5.5 cm1833°
5 cm2036°40'



Although accommodation and convergence are thus intimately linked tegether, it can very easily be proved that they may have a separate and independent action. If we suspend the accommodation with
atropine, the convergence is not interfered with; or an object at a certain distant being seen clearly without a glass, can still be seen distinctly with weak concave and convex glasses.

It may, therefore, be stated that although the accommodation and convergence are intimately associated, they may be independent or each other to a certain degree, so as to meet ordinary requirements;
thus the changes which take place during advancing life, when, for the same amount of convergence, a greater contraction of the ciliary muscle is necessary to produce the requisite change in the accommodation, owing to diminishing elasticity of the lens.

It is obvious also that the relations between accommodation and convergence must necesarily be very different in ametropia, and this relation will be again referred to when treating the varieties of ametropia in detail.

The following diagram (Fig. 34) shows the relative amount of accommodation for different points of convergence

FIG. 34.
in an emmetrope aged fifteen. The amount of accommodation in excess of the metrical angle of convergence is called positive, and the amount below negative.

The diagonal D D' represents the convergence from infinity to 5 cm. ; it is also a record of the accommodation. The line P P' P'' indicates the maximum accomodation for each point of convergence, and the line r r' the minimum. The numbers on the left and below the diagram are dioptres and metrical angles of convergence; thus, when the visual lines are parallel, it will be seen that 3-5 D. of positive accommodation can be put into play, i.e. the object can still be seen distinctly with a concave glass of that strength; 3.5 D. is therefore the relative amplitude of accommodation for convergence adapted to infinity; or the metrical angle of C being 5, which is a distance of 20 cm. away, the accommodation for that point
would equal 5 D.; the positive amount that can be put in force while the angle of C. remains the same would be 3 D., and the negative also 3 D., the object being seen clearly with a concave or convex glass of 3 D., therefore the relative amplitude of accommodation for
C 5 is 6 D. When the angle C = 10 or any larger angle, the accommodation that can be put in force will be seen to be entirely on the negative side.

Thus, the convergence being fixed, the amount of accommodation which can be brought into play for that particialar point is the sum of the difference between the strongest concave and convex glass
employed.

The eye being accommodated for an object at a certain distance, the amount of convergence for that particular point may be measured by placing in front of the eyes prisms bases outwards; the strongest with which the object is still seen singly is the measure of the positive part of the amplitude of convergence. Prisms, bases inwards, give us the negative part the sum of these is the amplitude of relative convergence.