Indian Journal of Ophthalmology

: 1972  |  Volume : 20  |  Issue : 4  |  Page : 153--157

Accommodative-convergence over accommodation (AC/A) ratio (in normal Indian subjects)

DK Sen, S.R.K Malik 
 Department of Ophthalmology Maulana Azad Medical College and Associated Hospitals, New Delhi, India

Correspondence Address:
D K Sen
Department of Ophthalmology Maulana Azad Medical College and Associated Hospitals, New Delhi

How to cite this article:
Sen D K, Malik S. Accommodative-convergence over accommodation (AC/A) ratio (in normal Indian subjects).Indian J Ophthalmol 1972;20:153-157

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Sen D K, Malik S. Accommodative-convergence over accommodation (AC/A) ratio (in normal Indian subjects). Indian J Ophthalmol [serial online] 1972 [cited 2022 Oct 7 ];20:153-157
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Full Text

Accommodation and convergence are inter-related and they develop together so that a single clear image is appreciated. The ratio accommoda­tive-convergence (AC) over accom­modation (A) indicates the relation­ship between the amount of con­vergence produced by a stimulus to accommodate and the amount of accommodation which produces that convergence. To see something clearly and singly at 1 metre, 1 metre angle of convergence between the two eyes and 1 dioptre of accommoda­tion are exerted. This is known as 1 : 1 relationship. Clinically, how­ever, it is easier to compare one person with another by measuring convergence in prism dioptres (P.D.). Six prism dioptres (P.D.) = 1 metre angle when the interpupillary distance (I.P.D.) is 60 mm. Therefore, to see clear as a single image at one metre, 6 P.D. of convergence and one dioptre of accommodation is being used. Two-thirds of this convergence that takes place (i.e. 4 Prism Dioptre) being accommodative the AC/A ratio becomes 4 : 1. This, however, is a theoretical concept. In practice AC/A ratio has been found to be variable even in normal persons (OGLE [9] ). The present study was carried out to find the range of values in normal Indian subjects.

 Methods and Materials

Under normal conditions, a stimulus to change the accommodation of the eye is accompanied by a change in the stimulus of convergence which is manifest as a change in the phoria of the eyes. The aim of measurement of the ratio should be to obtain the relationship between accommodative­convergence (AC) and accommoda­tion (A) when proximal and fusional convergence are eliminated. Of the several methods in use for the deter­mination of this ratio the following two methods were preferred because of their simplicity and accuracy. In both methods the ratio is determined by measuring the lateral deviation first without and then with the inter­position of spherical lenses. Concave lenses stimulate accommodation and thereby bring about corresponding change in the accommodative-con­vergence whereas convex lenses relax accommodation and cause a change in accommodative-convergence. The power of the spherical lenses is gradually increased to find out whether accommodative-convergence response is the same to each unit of accommodative stimulus. To start with we interposed both convex and concave spherical lenses for changing the accommodative stimulus but with convex lenses most of the persons experienced difficulty in relaxing accommodation proportionately. Res­ponse with convex lenses was conse­quently very irregular. It was also not possible to use concave lenses higher than 4.0 D as the persons complained of lot of discomfort and eye strain to keep the retinal image clear.

With any method it is of utmost importance to ensure that the person sees the target very clearly so that correct accommodation is exerted.

First Method: With the help of Maddox wing and Maddox rod.

The patient is asked to look at a fixed distance and the lateral devia­tion is measured firstly without any lens apart from the person's own correcting glasses if any and then with the interposition of lenses of identical power in front of each eye. The ratio is found out from the formula


Accommodative-convergence in prism dioptre; A = Accommodation in dioptre; ∆ L = deviation in prism dioptre when lenses are put; ∆ O = Original deviation in prism dioptre; D = power of lens used in dioptre.

As the distance is kept fixed the factor of proximal convergence is kept constant which, therefore, does not introduce any error in the results. Nature of this test is such that the factor of fusional convergence also does not come into the picture.

The procedure was carried out at a distance of 33 cm with the help of Maddox wing and at a distance of 1 metre with the help of Maddox rod. For each distance the first reading in prism dioptres was taken without any interposition of lenses and subsequent readings were taken after the interposition of - 1.0 D, -2.OD, -3.0D and -4.OD in succession.

Second Method: With the help of Synoptophore.

The patient was asked to wear his correcting glasses if any. Slide for measuring angle kappa was placed before one eye. A black vertical line was presented to the other eye. The patient was asked to bisect the zero by the black vertical line. Subjective angle was then noted in prism dioptres. The test was then repeated with the introduction of concave spherical lenses, - 1.0 D, - 2.OD, -3.0 D, and -4.0 D in succession and corresponding changes in the sub­jective angle reading were noted. Though the amount of proximal convergence is not completely eliminated in this method, the error introduced is negligible.

Fifty male and fifty female patients of various age groups ranging from six to sixty one years [Table 1],[Table 2] having normal visual acuity without or with correcting glasses were selected from eye O.P.D. of Maulana Azad Medical College and Associated Hospitals for this study. These patients had no ocular symptoms and reported to the eye O.P.D. for routine ophthalmic check-up.


On analysing the values statistically the ratio was found to be the same for the same individual at different viewing distances i.e. at 33 cm, 1 metre and infinity. It was observed that a unit change in the stimulus to accommodation resulted in a corres­ponding specific amount of change in the accommodative-convergence (i.e. the relationship between AC and A was linear) in 88 per cent of the cases with our first method and in 93 per cent. of the cases with the second method. Persons with decreased accommodative power due to presbyopia also showed this linear relationship.

From [Table 1],[Table 2] it is evident that AC/A ratio is independent of age and varies greatly from individual to individual. The maximum AC/A ration recorded in this series was 4 and the minimum 0.5. The mean value was 2.28 (average of 100 cases, both sexes). Out of 100 cases, in eleven the ratio was below 1.25, in 32 the ratio was found to be between 1.25 and 2 and in 45 cases between 2.25 and 3. Only 12 cases had the range between 3.25 and 4 [Table 3]. It is evident from [Table 1],[Table 2] that the ratio does not differ much in the two sexes, the mean values being 2.37 ± 0.009 in males and 2.19 ± 0.11 in females. How­ever, it appears as though it is slightly on the lower side in females.

Twenty subjects belonging to the various age groups were selected at random and AC/A ratio was deter­mined at intervals of 2 months over a period of 6 months. On statistical analysis of the data there was hardly any change of the values found in individual cases.

 Discussion and Comments

AC/A ratio can be measured sub­jectively and objectively. The objec­tive method can be used with ad­vantage in children and in persons with low intelligence, but the technique is not so simple. Subjective methods as described are simpler and quite accurate for clinical purposes.

The ratio is generally believed to be inborn and thought to remain constant throughout life. MORGAN AND PETERS, [8] MARTINS AND OGLE [7] and ALPERN AND LARSON [2] observed that reduction of the amplitude of accommodation associated with in­creased age is not associated with any significant change in the AC/A ratio. However, DAVIS AND JOSE [3] observed that AC/A ratio was almost constant till the age of 38 years; it then gradually increased till the age of 45 years and then it decreased. ALPERN AND HIRSCH [1] reported a gradual decrease of the ratio after the age of 25 years. Our study agrees with the observation of ALPERN AND LARSON [2] and MORGAN AND PETERS [8] and indicate that AC/A ratio is independent of age and sex and varies greatly from individual to individual. Repeated measurements of the ratio on 20 individuals over a period of six months points that AC/A ratio of a given normal individual is to a large extent a stable quantity which is at variance with the observa­tion of MANAS [6] who found that AC/A ratio was unstable. That this ratio is determined by heredity rather than by environmental factors is suggested by HOFSTETTER'S [4] study of the AC/A ratios of 30 pairs of identical twins. Because of this hereditary background the ratio has also been found to be variable from country to country. TAIT [10] found the highest and lowest ratios to be 5.4 and 1.0 respectively. Of his 35 cases in 29 the ratio ranged between 2.1 and 5.0. HUGHES [5] considered the ratio between 3 and 5 as normal. WYBAR [12] com­mented that as a general rule the ratio is between 3 and 5 in normal people with an average figure of about 4. In our series it has been found to vary between 0.5 and 4. In majority of the cases the ratio was between 2.25 and 3. It appears that in India the AC/A ratio is comparatively on the lower side. This explains our common observation that most of the normal persons who are essentially orthophoric at a distance of 6 meters do have some degree of exophoria at 33 cm.

The possibility of a non-linear response of AC to changes in the stimulus to A has been suggested by WESTHEIMER [11] principally on theore­tical grounds. He observed that it is difficult to understand how such a linearity is maintained in view of the complex nature of both the accom­modative and the convergence pro­cesses. However, MARTINS AND OGLE [7] demonstrated the linear rela­tionship in 92 per cent of normal individuals. We also found this linearity in majority of the cases. Observation of linearity also in presbyopic cases by MARTINS AND OGLE [7] as well as by us supports the view that it is the stimulus to accom­modation rather than the actual amount of accommodation that is important to bring about the accom­modative convergence.

This ratio has a great bearing in squint. If it is abnormally high, excessive accommodative-convergence is exerted on accommodative effort even when the hypermetropia is of small degree. A high ratio is, there­fore, found in patients with accom­modative squint of the convergence excess type. If this ratio is low, less accommodative convergence takes place on accommodation and the eyes will be relatively divergent. Therefore, for proper assessment of the role of AC/A ratio in a given case of squint, it is essential to be well acquainted with the normal variation of this ratio in a given population.


AC/A ratio was determined in 100 normal Indian subjects belonging to both sexes and different age groups by gradient and synoptophore methods.

The values ranged from 0.5 to 4. The mean value was 2.28. In majority of cases the ratio was between 2.25 and 3 which is com­paratively lower than that found in the Western population. The ratio was found stable, linear in 88-93 percent of cases and independent of age or sex of a person.


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