Defects of Vision

Optical instruments have application in human life. A simple microscope is used to view small objects clearly while the telescope is used to view distant objects. The main objective of those instruments is to see the objects better and completely.

Human Eye

The eye is nearly spherical in the shape of diameter about 2.5 cm. The front part of the lens is covered by a touch transparent membrane called cornea. Most of the refraction takes place at the cornea.
Behind the cornea, space is filled with a liquid called the aqueous humour and behind it, there remains a crystalline lens. The refractive index of this liquid is about 1.336. The front part of the lens is covered with a muscular diaphragm called iris, which has a small hole called the pupil.
The lens is a capsule containing a fibrous jelly which is hard at the centre and gradually softens at outer portions. It has a refractive index of 1.4337 on the average. The curvature of the lens can be changed with the help of ciliary muscles to see the object at various distances.
Most part of the eye behind the lens is filled with a liquid called vitreous humour, a liquid having a refractive index of 1.336. the light entering the eye forms an image on the retina which covers the inside of the rear part of the eyeball.

When relaxed, the normal eye sees an object at infinity, the focal point is at the retina. When the object is nearer to the eye, the lens forms more spherical in shape with the help of ciliary muscle and makes at the retina. The power of the lens can be adjusted with the help of ciliary muscles and the object at various distances can be seen. This process of the eye is called accommodation.

Defects of vision

Far and near point of eye
The extremes of range over which an eye can see objects distinctly are known as far point and near point of the eye. For a normal eye, the far point is infinity and near point is 25 cm from the eye as shown in the figure. The distance of the object at near point, i.e. 25 cm, is called the least distance of distinct vision.
When an eye cannot focus the light at the retina, the object cannot be seen clearly. Such defects of vision observed in the human eye are myopia or hypermetropia. The eye defect also appears due to the old age when the ciliary muscles are not able to control the curvature of the eye lens. This defect of the eye is called presbyopia. There is another type of eye defect called astigmatism which is due to uneven curvature of the cornea. As a result, the horizontal and vertical lines are not equally visible kept at a same distance.

Myopia

In this defect, the eye can see nearer objects clearly but it cannot see the distant objects clearly. The parallel rays of the from a distant object are focused at a point Q in front of the retina and clear image is not formed on the retina. So, the far point of the eye is shifted from infinity to a point P nearer to the eye as shown in the figure. This defect of vision is produced due to elongation of eye-ball or decrease in the focal length of the eye lens. This defect is also called short-sightedness, can be corrected by using a diverging lens of a suitable focal length.

Let x be the distance of for point for point from the eye. As the diverging lens forms the image of a distance object at the far point P of the eye, the image distance, v = -x and object distance, \( u = \infty \) . From the lens formula,
\begin{align*} \frac 1f &= \frac 1u + \frac 1v \\ &= \frac {1}{\infty } + \frac {1}{-x} \\ &= - \frac {1}{x} \\\text {or,} \: f &= -x \\ \end{align*}
Hence, the focal length of the two lens is equal to the distance of far point from the eye and the lens is diverging or concave.

Hypermetropia

In this defect, a person can see the distant objects nearer to the eye. The near point of such eye lies farther away from the least distance of distinct vision. This defect, also called long-sightedness, is produced due to short eyeball, as well as due to longer focal length of the eye lens. The rays from an object at normal near point are brought to focus at a point N behind the retina as shown in the figure. A convex lens is needed to correct this defect.

Let x be the distance of near point from the eye. For the convex lens, object distance u = D and image distance v = -x. The focal length of the lens is given by
$$ \frac 1f = \frac 1u + \frac 1v = \frac 1D - \frac 1x $$
Since x> D, f is positive. So, a converging lens is needed to correct this defect.

Visual Angle

When an object is viewed, the angle subtended by the object at the eye is known as a visual angle. A usual angle Ï´ made by an object is shown in the figure.

Suppose an object OA in front of the eye and its image formed on the retina is IB. The height of image is given by
\begin{align*} h’ = IB = \theta IL = \theta a \\ \text {where } \: IL = a, \text {Diameter of the eye. Since a is constant,} \\ h’ \propto \theta \\ \end{align*}
So, the size of image formed by the eye is proportional to the angle subtended by the object at the eye. Thus, if two objects of different sizes are lying at different distances from the eye, and they subtended the same angle at the eye, they will appear to be of the same size, as shown in the figure. Similarly, if an object lies at a different distance from the eye, it makes different distance from the eye, it makes different visual angles, and so, the size of the image is observed different as shown in the figure.