Click the right arrow to show an emmetropic eye, for comparison.
Click the left arrow to show a refractive hyperope, for comparison.
Hyperopia (also called hypermetropia) is a type of refractive error where the power of the eye’s optics is not enough to converge the light into focus on the retina. This means that a sharp image of a distant object forms slightly behind the retina. The light, when it hits the retina, has not yet converged fully and is spread out, so the image formed on the retina is blurred.
There are two main kinds of hyperopia. In the first kind, called refractive hyperopia, the length of the eye is normal, but the power of the cornea and crystalline lens are together somewhat less than normal, perhaps because the cornea is not as curved as it should be. ( Figure 1).
Click the right arrow to show an emmetropic eye, for comparison.
Click the left arrow to show a refractive hyperope, for comparison.
The other way an eye can be myopic is if it is too short ( Figure 2); then the retina is closer to the lens than it should be. The light leaving the eye converges to where the retina should be (shown by the white dot), but the retina is actually a little closer. The eye's optics in this case are normal, but they are too weak for a shorter eye, which requires more power. This is called axial hyperopia, because the eye's optic axis is shorter than it should be. This is the most common form of hyperopia.
Click the right arrow to show an emmetropic eye, for comparison.
Click the left arrow to show an axial hyperope, for comparison.
Accommodation is a complicating factor in hyperopia. A hyperopic eye has less power than it requires, but accommodation can be used to increase power and counteract some, if not all, of the hyperopia of an eye. We will ignore accommodation to begin with.
The far point in hyperopia is a slightly more abstract idea than for myopia. For a myope, if you place an object at their far point, they can see the object clearly. If you put an object at the far point of a hyperope, they won’t be able to see it, because the far point for a hyprope is actually behind their eye.
A myopic eye needs divergent light striking the cornea in order to see clearly. A hyperopic eye (unaccommodated) needs convergent light in order to see clearly. The convergence of the light hitting the cornea that lets the hyperopic eye form a clear image is the ocular refraction, as before. The far point of the hyperopic eye is one over the ocular refraction (as before). This far point is is where the convergent light hitting the hyperopic eye would converge to if the eye were not in the way ( Figure 3). Thus the difference between the myopic and hyperopic far point is that, for the myope, light diverges from the far point, whereas for the hyperope, light converges towards the far point.
For the eye in the figure, when the far point is about \( 0.076-0.079\text{m} \) away, the convergence of the light hitting the cornea is sufficiently high for the hyperopic eye to finish converging it on the retina.
For a hyperope to see distant objects clearly, we must change the vergence of light from a distant object (which is zero) to equal the ocular refraction by the time it hits the cornea. This can be done with a positive lens.
Understanding how a spectacle lens can correct hyperopia involves noticing two things:
A hyperopic eye will be able to focus light onto the retina (i.e. see clearly) when the light hitting it is converging towards the far point.
When light from a distant object (vergence = 0) strikes a positive lens, the light leaving the lens will converge towards the lens’s focal point (Chapter 2).
Suppose then that we carefully place a positive lens in front of the hyperopic eye so that the focal point of the lens is in exactly the same place as the far point of that eye. The light from the lens, just before it hits the eye, is converging towards the focal point of the lens. But this is also the same place as the far point, so the light is converging towards the far point. In that case, the hyperopic eye will be able to focus the light onto the retina.
This is shown in Figure 4.
In the bottom diagram, parallel light from a distant object is converged by a positive lens towards the focal point of the lens, which in this case is \( 0.09\text{m} \) from the lens. When the lens is moved so that its focal point coincides with the far point, the convergence of the light, when it hits the eye, is exactly what the eye needs for clear vision.
The fact that the far point of the eye and the focal length of the spectacles must coincide gives a simple relationship between the far point distance, the focal length, and the distance from spectacles to eyes: The focal length of the lens must equal the distance from lens to eye plus the distance from eye to far point. That is,
This is identical to the spectacle equation for the myope, but here both the far point distance and the spectacle focal length are positive (they are both negative for the myope).
A hyperope with an ocular refraction of \( +6.5\text{D} \) wears spectacles with a spectacle distance of 14mm. What is the power of the spectacles?
Since all the relevant dimensions are positive, we don't really need a diagram to keep things straight for a hyperope.
The distance to the far point is \( 1/6.5=0.154\text{m} \) . The spectacle focal length is thus \( 0.154+0.014=0.168\text{m} \). The spectacle power is then \( 1/0.168=+5.95\text{D} \).
A patient has spectacles with power \( +8.5\text{D} \) worn at a distance of \( 13\text{mm} \). What power of contact lenses should they have?
To answer this, first work out the far point distance. The focal length of the spectacles is \( 1/8.5=0.118\text{m} \), and so the distance from the eye to the far point is \( 0.118\text{m} \) less the spectacle distance, or \( 0.118 - 0.013 = 0.105\text{m} \). Contact lenses have a spectacle distance of zero, so the focal length of the contacts is exactly the same as the far point distance. Thus the power of the contacts should be \( 1/0.105=+9.52\text{D} \).
It is always the case for a hyperope that the contact lens prescription is stronger than the spectacle prescription. The difference between the two prescriptions increases with the amount of correction required.
Because accommodation increases the power of the eye it is possible for hyperopes to compensate for their lack of optical power by accommodating. For example, if the ocular refraction of a hyperope is \( +3\text{D} \), that means they need roughly \( 3\text{D} \) more power to see distant objects clearly. If they have enough accommodative amplitude, they can easily supply this extra power by accommodating. Thus hyperopes can often see distant objects clearly, if they have sufficient accommodation, whereas myopes never can.
Since the hyperope can see distant objects, they will not initially complain that their distance vision is impaired. Instead, they will complain that they cannot focus clearly on near objects. This is because they have already used up some of their accommodation to correct their hyperopia so they have less left to focus on near objects. As a result, their near point is further away than normal.
The amount of hyperopia that the patient can eliminate by accommodating is called the facultative hyperopia. The amount of hyperopia left over (if any) is called the absolute hyperopia. The total hyperopia is the sum of facultative and absolute:
The total hyperopia is the same as the ocular refraction.
A patient with a total hyperopia of \( +5\text{D} \) and an amplitude of accommodation of \( 8\text{D} \) can use \( 5\text{D} \) of their accommodation to correct all of their hyperopia. Thus their facultatitive hyperopia is \( +5\text{D} \) and their absolute hyperopia is \( 0 \). However, having used up \( 5\text{D} \) of accommodation means they only have \( 3\text{D} \) of accommodation left, so their near point is then \( 1/3=0.333 \)m.
A patient has a total hyperopia of \( +6\text{D} \) but their accommodative amplitude is only \( 3\text{D} \) (perhaps because they are older). If they accommodate fully, that will only remove \( 3\text{D} \) of hyperopia, leaving \( 3\text{D} \) remaining. The amount of hyperopia compensated by accommodation, \( 3\text{D} \), is their facultative hyperopia; the remaining \( 3\text{D} \) of hyperopia is their absolute hyperopia. Unfortunately for this patient their near point doesn’t exist (as they have no accommodation left over), so they can see nothing clearly.
The facultative and absolute components of hyperopia can be determined by subjective refraction:
Take Example 3 above. Since the patient can already see clearly at distance, the lowest plus power that enables them to see the 6/6 line on the letter chart is \( 0\text{D} \), which is their absolute hyperopia. When the plus power is \( +5\text{D} \), then this completely corrects their hyperopia and the patient does not need to accommodate. If we increase past this, however, their hyperopia has been overcorrected and they will not be able to see the letter chart clearly.
| Added correction | Accommodation used | Resultant Refractive Error | VA |
|---|---|---|---|
| plano (0D) | 5D | 0D | 6/6 |
| +1D | 4D | 0D | 6/6 |
| +2D | 3D | 0D | 6/6 |
| +3D | 2D | 0D | 6/6 |
| +4D | 1D | 0D | 6/6 |
| +5D | 0D | 0D | 6/6 |
| +6D | 0D | -1D | 6/12 |
Table 1. An example of what happens as successively higher powered positive lenses are placed in front of a hyperopic eye with a refractive error of \( +5\text{D} \). The table assumes that \( 1\text{D} \) of refractive error causes a drop of 3 lines in a Snellen chart. Note that the sequence of added corrections is illustrative only - you wouldn’t restrict yourself to round-number powers in practice.
This is shown in Table 1. (The “resultant refractive error” column is the total hyperopia less the added correction and the accommodation used.) What is happening here is that each dioptre of added correction is reducing the need for accommodation by the same amount. So long as the correction plus accommodation adds up to the total hyperopia ( \( +5\text{D} \)) the patient acts as if they have no refractive error. When the added correction goes over the total hyperopia, the accommodation can go no lower than zero, and as a result the patient can no longer see the letter chart clearly. The lowest added correction that lets the patient see the letter chart is \( 0\text{D} \), which is their absolute hyperopia. The highest plus power that lets the patient see the letter chart, \( +5\text{D} \), is their total hyperopia.
| Added correction | Accommodation used | Resultant Refractive Error | VA |
|---|---|---|---|
| +1D | 3D | 2D | 6/24 |
| +2D | 3D | 1D | 6/12 |
| +3D | 3D | 0D | 6/6 |
| +4D | 2D | 0D | 6/6 |
| +5D | 1D | 0D | 6/6 |
| +6D | 0D | 0D | 6/6 |
| +7D | 0D | -1D | 6/12 |
Table 2. This patient has some absolute hyperopia. As a result, they require some additional plus power (+3D) in order to see the 6/6 line clearly.
Doing the same for Example 4 yields Table 2. In this case, \( +3\text{D} \) is the smallest correction that allows the patient to see the 6/6 line on the letter chart; this is their absolute hyperopia. The largest correction that allows the patient to see the letter chart, \( +6\text{D} \), is their total hyperopia.
In young hyperopes, it is not unusual to find that the refractive error is greater when measured using objective methods (retinoscopy) or under cycloplegia, than when measured using subjective methods. The reason for this is because when doing subjective refraction (e.g. by finding the maximum plus sphere that gives good distance vision) the young hyperopic eye does not completely relax its accommodation, whereas under retinoscopy conditions it does, or at least relaxes more. (Why retinoscopy should lead to more relaxed accommodation is unknown.) Even with retinoscopy, there remains some unrelaxed accommodation, so in order to get the total hyperopia, it is necessary to paralyze the ciliary muscles with a cycloplegic drug while doing retinoscopy.
The hyperopia that is measured by subjective methods is called the manifest hyperopia . The difference between subjective and objective (preferably cycloplegic) refraction is called the latent hyperopia. Total hyperopia is the sum of latent and manifest hyperopia. Latent hyperopia is a component of the facultative hyperopia, since it is caused by accommodation.
The accommodative amplitude of a hyperope is the difference in vergences from the far point and the near point. This difference shows how much the hyperope can change the power of their optics to retain a sharp image on the retina.
This is exactly the same as the myope and emmetrope.
A hyperopic patient has a far point which is 0.25m behind their eye, and a near point which is 0.5m in front of their eye. What is their amplitude of accommodation?
The vergence at the far point is \( 1/0.25 = +4\text{D} \) . The vergence at the near point is \( 1/(-0.5)=-2\text{D} \) , so the difference is \( 4-(-2)=6\text{D} \).
Another way of thinking about this calculation is that the patient uses \( 4\text{D} \) of accommodation to see a distant object (since their ocular refraction is \( 1/0.25=4\text{D} \)), and then uses an additional \( 2\text{D} \) to overcome the divergence of light from the near point. The total is \( 4+2=6\text{D} \) of accommodation.