Convergence and Divergence (2024)

In order for you to look at an object as it moves closer to your face, the eyes must rotate inward (converge) toward the object. When looking at a faraway object, they move by rotating outwards towards the ears or diverge. Convergence and divergence are unique eye movements as these are the only eye movements that are not conjugate (meaning the eyes move in the same direction) but are instead termed disconjugate. The brain is constantly rapidly sampling the visual environment, quickly altering between convergence and divergence, then just as quickly holding eye posture so that the image of interest is stabilized on the retina.

Convergence

Convergence is the ability to turn the two eyes inward toward each other to look at a close object. We depend on this visual skill for near-work activities such as desk work at school, working on a smartphone type device, or even in sports when catching a ball.

Convergence requires a coordinated stimulation of some extraocular muscles at the same time others are relaxed. Convergence occurs by stimulation of the medial rectus muscle of both eyes (third cranial [oculomotor] nerve) while simultaneously relaxing the lateral recti (sixth cranial [abducens] nerve).

More than just simple eye movements occur with convergence. When the eyes converge, the focusing (accommodative) system is engaged, and the pupils get slightly smaller. This set of three processes - technically termed convergence, accommodation, and miosis - is known as the near triad.

Divergence

Divergence is the opposite of convergence and is the ability to turn the two eyes outwards to look at a distant object. We depend on this skill for distance activities such as reading the board at school, driving and watching TV.

To diverge, the opposite of the near triad must occur. Now the eyes diverge, accommodation is inhibited, and the pupils slightly dilate.

What if I Have Trouble Converging or Diverging?

Your optometrist may perform a simple eye test. This test is called the near point of convergence (NPC). This test measures the ability of the patient to keep a target single as it moves closer to the nose. Think of this as the distance from your eyes to the point where both eyes are just unable to maintain focus and start to experience double vision. To perform this test, a clinician will use a small penlight or other fixation target and then slowly move the light towards the patient. The patient is to report when the light breaks into two lights (double vision). The penlight is then moved farther away and the patient is asked when the recovery point (resolution of double vision) occurs.

Some patients struggle with convergence or divergence. Convergence insufficiency (CI) is one of the most common disorders of binocular vision; CI affects approximately 5% of children in the United States and may have a serious impact on an individual's performance in school, choice of jobs, and quality of life. Patients that suffer from CI are unable to keep the eyes converged for an extended period of time. Convergence excess is the opposite of CI. Here a patient over-convergences, which may cause pulling or straining sensations, or an inward eye turn.

Divergence insufficiency is the inability of the eyes to properly and fully diverge. The opposite of divergence insufficiency is divergence excess. Divergence excess is an over-divergence when attempting to look at distant objects.

These conditions that affect convergence or divergence may cause symptoms such as seeing double at near or far while viewing an object. Common symptoms include:

  • headaches
  • blurred vision
  • double vision
  • eye strain or fatigue
  • sore or watery eyes after a near or far task
  • words moving about on a page while reading
  • frequenting losing your place while reading

What is it Like to have Convergence Insufficiency?

Reading is a great example of a task that requires normal convergence.

Convergence and Divergence (1)

To read, the eyes must rotate inward, the focusing system must engage, and a series of tracking movements are used to move the eyes across a page.

Convergence and Divergence (2)

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But, if the eyes are unable to maintain a converged position, reading becomes quite difficult! Words may become blurry, doubled, or appear to move around on the page. The end result is often fatigue, headache, and likely avoidance of near work.

Can Convergence or Divergence Problems be Treated?

In short, absolutely. Treatment often focuses on working the ability of the eyes to converge and focus at different distances. Vision therapy uses a series of activities to build up progressively the ability to converge, diverge, and the rapidly alternate between convergence and divergence.

Let's use a VR example. Barnyard Bounce is a game designed to treat convergence insufficiency. In this game, the patient adjusts the horizontal position of a chicken and tries to match the chicken with an egg. In our example, the chicken is visible only in the left eye and the egg is shown only to the right eye (watch the video of the actual task here).

Convergence and Divergence (3)

In the above example, the patient must match their convergence ability to the location of the chicken and egg in the VR headset. If the patient's convergence ability is good enough to meet the convergence amount needed in the headset, the chicken and egg match perfectly! The top-left image is the projected location of the chicken/egg images, while the image in the screen to the left shows what the patient's brain interprets the image as.

Convergence and Divergence (4)

However, look at what happens if a patient is unable to converge to match the convergence amount needed in the game. Although the patient may perceive the images as overlapping, the actual location of the images is rather far apart.

When Should I see my Eye Care Professional?

The American Optometric Association recommends seeing your eye care professional for routine eye examinations every one to two years, depending on your age, symptoms, and health. If you're experiencing any of the symptoms mentioned above, your eye care professional may suggest vision therapy or may refer you to a behavioral optometrist that specializes in the treatment of binocular disorders. A vision therapy program often includes in-office and at-home therapy activities.

References

https://www.mayoclinic.org/diseases-conditions/convergence-insufficiency/diagnosis-treatment/drc-20352739

https://www.aoa.org/patients-and-public/caring-for-your-vision/comprehensive-eye-and-vision-examination/recommended-examination-frequency-for-pediatric-patients-and-adults

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Convergence and Divergence (2024)

FAQs

Convergence and Divergence? ›

Divergence generally means two things are moving apart while convergence implies that two forces are moving together. In the world of economics, finance, and trading, divergence and convergence are terms used to describe the directional relationship of two trends, prices, or indicators.

How do you tell if a function is convergent or divergent? ›

Notice that a sequence converges if the limit as n approaches infinity of An equals a constant number, like 0, 1, pi, or -33. However, if that limit goes to +-infinity, then the sequence is divergent.

What is the difference between convergence and divergence zones? ›

Divergence occurs when horizontal winds cause a net outflow of air from a region (more air leaving a vertical column of air than entering), while convergence occurs when horizontal winds cause a net inflow of air into a region (more air entering a vertical column than leaving it).

How do you tell if a series converges or diverges? ›

Definitions and Formulas for How to Determine Whether a Series Converges or Diverges By Using a Test. Convergent/Divergent Series: A series ∑ n = 1 ∞ a n converges if the limit lim k → ∞ ∑ n = 1 k a n exists and is a real number; otherwise, the series ∑ n = 1 ∞ a n is divergent.

What is convergence and divergence for dummies? ›

A convergent sequence has a limit — that is, it approaches a real number. A divergent sequence doesn't have a limit. Thus, this sequence converges to 0. In many cases, however, a sequence diverges — that is, it fails to approach any real number.

What is the difference between function convergence and divergence? ›

A convergent function is a function that approaches a set limit (i.e., it has a horizontal asymptote). A divergent function is a function that does not approach a set limit (i.e., no horizontal asymptote).

How do you determine divergence? ›

The divergence is generally denoted by “div”. The divergence of a vector field can be calculated by taking the scalar product of the vector operator applied to the vector field. I.e., ∇ . F(x, y).

What is the example of convergence and divergence? ›

Divergent series typically go to ∞, go to −∞, or don't approach one specific number. An easy example of a convergent series is ∞∑n=112n=12+14+18+116+⋯ The partial sums look like 12,34,78,1516,⋯ and we can see that they get closer and closer to 1.

What is the main difference between convergent and divergent boundaries? ›

Convergent boundaries have plates that move towards each other, whereas divergent boundaries have plates that move away. Both convergent and divergent boundaries can create mountains and volcanos although the geology of how these features form is different.

How do you describe convergence? ›

Convergence is when two or more things come together to form a new whole, like the convergence of plum and apricot genes in the plucot. Convergence comes from the prefix con-, meaning together, and the verb verge, which means to turn toward.

How do you quickly tell if an integral converges or diverges? ›

If the limit exists and is a finite number, we say the improper integral converges . If the limit is ±∞ or does not exist, we say the improper integral diverges .

How do you know if an equation diverges? ›

If the denominator has a higher degree, then the sequence converges to 0; if the numerator has a higher degree, then the sequence diverges to ∞ if the leading coefficients have the same sign, or to −∞ if they have different signs.

Does a series always either converge or diverge? ›

Convergence means that the infinite limit exists

A sequence always either converges or diverges, there is no other option. This doesn't mean we'll always be able to tell whether the sequence converges or diverges, sometimes it can be very difficult for us to determine convergence or divergence.

What is convergence and divergence math is fun? ›

Convergent sequence is when through some terms you achieved a final and constant term as n approaches infinity . Divergent sequence is that in which the terms never become constant they continue to increase or decrease and they approach to infinity or -infinity as n approaches infinity.

What is the difference between convergence and divergence English? ›

Convergence is when individuals change their speech to sound more like others, whereas divergence is when they accentuate differences. People can upward converge/diverge by making themselves appear more upper class. Or, they can downward converge/diverge by making themselves appear more working class.

How does divergent thinking differ from convergent thinking? ›

Summary. Convergent thinking focuses on finding one well-defined solution to a problem. Divergent thinking is the opposite of convergent thinking and involves more creativity. In this piece, we'll explain the differences between convergent and divergent thinking in the problem-solving process.

How do you prove a function is divergent? ›

To show divergence we must show that the sequence satisfies the negation of the definition of convergence. That is, we must show that for every r∈R there is an ε>0 such that for every N∈R, there is an n>N with |n−r|≥ε.

How do you identify a convergent series? ›

If the sequence of partial sums is a convergent sequence (i.e. its limit exists and is finite) then the series is also called convergent and in this case if limn→∞sn=s lim n → ∞ ⁡ s n = s then, ∞∑i=1ai=s ∑ i = 1 ∞ a i = s .

What is the difference between divergent and convergent examples? ›

Solving an algebraic equation that has one correct answer is an example of convergent thinking. Composing music and writing creative lyrics to the music shows divergent thinking. One correct solution to a problem. No room for ambiguity.

How do you know if a function is conditionally convergent? ›

In a conditionally converging series, the series only converges if it is alternating. For example, the series 1/n diverges, but the series (-1)^n/n converges.In this case, the series converges only under certain conditions. If a series converges absolutely, it converges even if the series is not alternating.

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