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Defects of Vision and Their Correction: Explanation, Diagram And Example Problems
The ability to see is called vision. It is also called eyesight. Vision is known as ‘drishti’ in Hindi. Sometimes the eye of a person cannot focus the image of an object on the retina properly. In such cases the vision of a person becomes blurred and he cannot see either the distant objects or nearby objects (or both) clearly and comfortably.
The person is said to have a defect of vision. The defects of vision are also known as defects of eye. There are three common defects of vision (or defects of eye). These are :
- Myopia (Short-sightedness or Near-sightedness)
- Hypermetropia (Long-sightedness or Far-sightedness), and
- Presbyopia.
These are the refractive defects of vision because they are caused by the incorrect refraction of light rays by the eye-lens. These defects of vision can be corrected by using suitable spherical lenses (convex lenses or concave lenses). These lenses are usually used in the form of eye-glasses or spectacles (see Figure). We will now describe all these defects of vision and their correction, one by one. Let us start with myopia.
1. Myopia (Short-sightedness or Near-sightedness)
A short-sighted person means that the short sight of the person (to see nearby objects) is normal but his long-sight (to see distant objects) is defective. Myopia (or short-sightedness) is that defect of vision due to which a person cannot see the distant objects clearly (though he can see the nearby objects clearly).
For example, a child having the defect called myopia (or short-sightedness) and sitting on the back benches in the class cannot read the writing on blackboard clearly though he can read his book comfortably. The far point of an eye suffering from myopia is less than infinity. Such a person can see clearly only up to a distance of few metres (or even less).
The defect of eye called myopia (or short-sightedness) is
- due to high converging power of eye-lens (because of its short focal length), or
- due to eye-ball being too long.
In some cases, in an eye suffering from myopia, the ciliary muscles attached to the eye-lens do not relax sufficiently to make the eye-lens thinner to reduce its converging power. So, due to the greater converging power of the eye-lens in myopic eye, the image of a distant object is formed in front of the retina and hence the eye cannot see it clearly.
In other cases, in the eye suffering from myopia, the eye-ball is too long due to which the retina is at a larger distance from the eye-lens. This condition also results in the formation of the image of a distant object in front of the retina (even though the eye-lens may have correct converging power).
Figure (a) shows an eye having the defect called myopia (or short-sightedness). In this case, the parallel rays of light coming from the distant object O (at infinity) are converged to form an image I in front of the retina due to which the eye cannot see the distant object clearly [see Figure (a)] (The object is at a large distance called infinity from the eye, so it has not been shown in this Figure).
The image is formed in front of the retina either due to high converging power of eye-lens or due to eye-ball being too long.
The far point of eye having myopia (or short-sightedness) is at point F which is less than infinity [see Figure (b)]. Please note that the rays of light coming from the person’s far point F can just be focused by his eye on the retina as shown in Figure (b).
This means that if the distant object can be made to appear as if it were at the far point F of this eye, then the eye can see it clearly. This is done by putting a concave lens in front of the eye (as described below).
Myopia (short-sightedness or near-sightedness) is corrected by using spectacles containing concave lenses. When a concave lens (diverging lens) L of suitable power is placed in front of the myopic eye as shown in Figure (c), then the parallel rays of light coming from the distant object (at infinity) are first diverged by the concave lens.
Due to this the concave lens forms a virtual image of the distant object at the far point F of this myopic eye [see Figure (c)]. Since the rays of light now appear to be coming from the eye’s far point (F), they can be easily focused by the eye-lens to form an image on the retina [see Figure (c)].
Please note that the concave lens used for correcting myopia should be of such a focal length (or power) that it produces a virtual image of the distant object (lying at infinity) at the far point of the myopic eye.
It should also be noted that the whole purpose of using a concave lens here is to reduce the converging power of the eye-lens. The concave lens used here decreases the converging power of the eye-lens and helps in forming the image of distant object on the retina of the myopic eye.
Calculation of Power of Concave Lens to Correct Myopia. The focal length of concave lens needed to correct myopia (or short-sightedness) in a person is calculated by using the lens formula \(\frac{1}{v}\) – \(\frac{1}{u}\) = \(\frac{1}{f}\).
In this formula, the object distance u is to be taken as infinity (∞), and the image distance v will be the distance of person’s far point (which is different for different persons). Knowing the focal length of the concave lens, we can calculate its power. This will become more clear from the following example.
Example Problem.
The far point of a myopic person is 80 cm in front of the eye. What is the nature and power of the lens required to correct the defect ?
Solution:
The defect called myopia is corrected by using a concave lens. So, the person requires concave lens spectacles. We will now calculate the focal length of the concave lens required in this case. The far point of the myopic person is 80 cm. This means that this person can see the distant object (kept at infinity) clearly if the image of this distant object is formed at his far point (which is 80 cm here). So, in this case : Object distance, u = ∞ (Infinity)
Image distance, v = – 80 cm (Far point, in front of lens)
And, Focal length, f = ? (To be calculated)
Putting these values in the lens formula :
\(\frac{1}{v}\) – \(\frac{1}{u}\) = \(\frac{1}{f}\)
we get \(\frac{1}{-80}\) – \(\frac{1}{\infty}\) = \(\frac{1}{f}\)
or – \(\frac{1}{80}\) – 0 = \(\frac{1}{f}\) (Because \(\frac{1}{\infty}\) = 0)
– \(\frac{1}{80}\) = \(\frac{1}{f}\)
f = – 80 cm
Thus, the focal length of the required concave lens is 80 cm. We will now calculate its power. Please note that the focal length of, – 80 cm is equal to \(\frac{-80}{100}\) m or – 0.8 m. Now,
Power, P = \(\frac{1}{f \text { (in metres) }}\)
= \(\frac{1}{-0.8}\)
= – \(\frac{10}{8}\)
= -1.25 D
So, the power of concave lens required is, -1.25 dioptres.
2. Hypermetropia (Long-sightedness or Far-sightedness)
A long-sighted person means that the long-sight of the person (to see distant objects) is normal but his short-sight (to see nearby objects) is defective. Hypermetropia (or long-sightedness) is that defect of vision due to which a person cannot see the nearby objects clearly (though he can see the distant objects clearly).
For example, a person having the defect hypermetropia cannot read a book clearly and comfortably though he can read the number of a distant bus clearly. The near-point of a hypermetropic eye is more than 25 centimetres away. Such a person has to hold the reading material (like a book or newspaper) at an arm’s length, much beyond 25 cm from the eye for comfortable reading. Please note that hypermetropia is just the opposite of myopia.
The defect of eye called hypermetropia (or long¬sightedness) is caused :
- due to low converging power of eye-lens (because of its large focal length), or
- due to eye-ball being too short.
In some cases, the ciliary muscles attached to the eye- lens become weak and cannot make the eye-lens thicker to increase its converging power. So, due to the low converging power of eye-lens in an eye suffering from hypermetropia, the image of nearby object is formed behind the retina and hence the eye cannot see it clearly.
In other cases, in an eye suffering from hypermetropia, the eye-ball is too short due to which the retina is at a smaller distance from the eye-lens. This condition also results in the formation of the image of a nearby object behind the retina (even though the eye-lens may have correct converging power).
Figure (a) shows an eye having the defect called hypermetropia (or long-sightedness). In this case the diverging rays of light coming from a nearby object O placed at the normal near point N (25 cm from the eye) are converged to form an image I behind the retina due to which the eye cannot see the nearby object clearly [see Figure (a)].
The image is formed behind the retina either due to low converging power of eye- lens or because of eye-ball being too short.
The near-point of an eye having hypermetropia (or long-sightedness) is at point N’ which is more than 25 centrimetres away [see Figure (c)]. The diverging rays of light coming from a hypermetropic person’s near point can just be focused by his eye on the retina as shown in Figure (b).
This means that if the object placed at the normal near point N (25 cm) can be made to appear as if it were placed at this eye’s near point AT, then the eye will be able to see it clearly. This can be done by putting a convex lens in front of the eye.
Hypermetropia (long-sightedness or far-sightedness) is corrected by using spectacles containing convex lenses. When a convex lens (converging lens) L of suitable power is placed in front of the hypermetropic eye as shown in Figure (c), then the diverging rays of light coming from the nearby object (at 25 cm) are first converged by this convex lens.
Due to this, the convex lens forms a virtual image of the nearby object (which is lying at the normal near point N) at the near point N’ of the hypermetropic eye [see Figure (c)]. Since the rays of light now appear to be coming from this eye’s near point N’, they can be easily focused by the eye-lens to form an image on the retina [see Figure (c)].
Please note that the convex lens used for correcting hypermetropia (or long-sightedness) should be of such a focal length (or power) that it forms a virtual image of the object (placed at the normal near point N of 25 cm), at the near point N’ of the hypermetropic eye.
It should also be noted that the whole purpose of using a convex lens here is to increase the converging power of the eye-lens. The convex lens used in spectacles increases the converging power of eye-lens and helps in forming the image of a nearby object on the retina of the eye.
Calculation of the Power of Convex Lens to Correct Hypermetropia. The focal length of convex lens needed to correct hypermetropia (or long-sightedness) can be calculated by using the lens formula \(\frac{1}{v}\) – \(\frac{1}{u}\) = \(\frac{1}{f}\).
In this formula, the object distance u is to be taken as the normal near point of the eye (which is 25 cm) and the image distance v will be the distance of the near point of the hypermetropic eye. Knowing the focal length of the convex lens, its power can be calculated. This will become more clear from the following example.
Example Problem.
The near point of a hypermetropic eye is 1 m. What is the nature and power of the lens required to correct this defect ? (Assume that the near point of the normal eye is 25 cm).
Solution:
The eye defect called hypermetropia is corrected by using a convex lens. So, the person requires convex lens spectacles. We will first calculate the focal length of the convex lens required in this case. This hypermetropic eye can see the nearby object kept at 25 cm (at near point of normal eye) clearly if the image of this object is formed at its own near point which is 1 metre here. So, in this case :
Object distance, u = -25 cm (Normal near point)
Image distance, v = -1 m (Near point of this defective eye)
= -100 cm
And, Focal length, f = ? (To be calculated)
Putting these values in the lens formula,
\(\frac{1}{v}\) – \(\frac{1}{u}\) = \(\frac{1}{f}\)
We get : \(\frac{1}{-100}\) – \(\frac{1}{-25}\) = \(\frac{1}{f}\)
or – \(\frac{1}{100}\) – \(\frac{1}{25}\) = \(\frac{1}{f}\)
\(\frac{-1+4}{100}\) = \(\frac{1}{f}\)
\(\frac{3}{100}\) = \(\frac{1}{f}\)
f = \(\frac{100}{3}\)
f = 33.3 cm
Thus, the focal length of the convex lens required is +33.3 cm. We will now calculate the power. Please note that 33.3 cm is equal to \(\frac{33.3}{100}\) m or 0.33 m. Now,
Power, P = \(\frac{1}{f \text { (in metres) }}\)
= \(\frac{1}{+0.33}\)
= + \(\frac{100}{33}\)
= +0.33
So, the power of convex lens required is +3.0 dioptres.
Myopia and hypermetropia are the two most common defects of vision (or defects of eye). We will now study another defect of vision which occurs in old age. It is called presbyopia.
3. Presbyopia
In old age, due to ciliary muscles becoming weak and the eye-lens becoming inflexible (or rigid), the eye loses its power of accommodation. Because of this an old person cannot see the nearby objects clearly. This leads to the defect called presbyopia. Presbyopia is that defect of vision due to which an old person cannot see the nearby objects clearly due to loss of power of accommodation of the eye.
For example, an old person having presbyopia cannot read a book or newspaper comfortably and clearly without spectacles. Presbyopia occurs in old age due to the gradual weakening of the ciliary muscles and diminishing flexibility of the eye-lens. The near-point of the old person having presbyopia gradually recedes and becomes much more than 25 centimetres away.
Actually, presbyopia is a special kind of hypermetropia. We can call it old age hypermetropia. Presbyopia is the hypermetropia (or long-sightedness) caused by the loss of power of accommodation of the eye due to old age. Presbyopia defect is corrected in the same way as hypermetropia by using spectacles having convex lenses (see above Figure).
It is also possible that the same person has both the defects of vision – myopia as well as hypermetropia. A person suffering from myopia as well as hypermetropia uses spectacles having bifocal lenses in which upper part consists of a concave lens (to correct myopia) used for distant vision and the lower part consists of a convex lens (to correct hypermetropia) used for reading purposes (see Figure).
These days it is possible to correct the refractive defects of the eye (such as myopia and hypermetropia) by using contact lenses or by undergoing surgical procedures. Then there is no need to wear spectacles.
Cataract
A yet another defect of the eye which usually comes in old age is the cataract. The medical condition in which the lens of the eye of a person becomes progressively cloudy resulting in blurred vision is called cataract. Cataract develops when the eye-lens of a person becomes cloudy (or even opaque) due to the formation of a membrane over it.
Cataract decreases the vision of the eye gradually. It can even lead to total loss of vision of the eye. The vision of the person can be restored after getting surgery done on the eye having cataract. The opaque lens is removed from the eye of the person by surgical operation and a new artificial lens is inserted in its place. Please note that the eye-defect called ‘cataract’ cannot be corrected by any type of spectacle lenses.