The ciliary muscles control the curvature of the lens in the eye and hence can alter the effective focal length of the system.

When the muscles are fully relaxed, the focal length is maximum.

When the muscles are strained, the curvature of the lens increases and focal length decreases.

For a clear vision, the image must be formed on the retina. The image distance is, therefore, fixed for clear vision and it equals the distance of the retina from the eye lens i.e 2.5 cm for a grown – up person.

\frac{1}{{\rm{v}}}\, + \,\frac{1}{u}\, = \,\frac{1}{f}\\
\frac{1}{u}\, = \,\frac{1}{f}\, - \,\frac{1}{{\rm{v}}}

Here v is fixed, hence by changing ‘f ’, the eye can be focussed on objects placed at different values of u.Thus, if f increases, u increases and vice – versa.

The maximum distance we can see is

\frac{1}{{{u_{\max }}}}\, = \,\frac{1}{{{f_{\max }}}}\, - \,\frac{1}{{\rm{v}}}

{f_{\max }}\, = \,maximum focal length possible for the eye lens.

For a normal eye,

{f_{\max }} = distance v i.e from lens to retina.

Thus {\rm{v}}\, = \,{f_{\max }}

\therefore \,\,\,\,\frac{1}{{{u_{\max }}}}\,\, = \,\,\frac{1}{{{f_{\max }}}}\,\, - \,\,\frac{1}{{{f_{\max }}}}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,0\\
\,or\,\,{u_{\max }}\, = \,\infty 

A person can theoretically have clear vision of objects situated at any large distance from the eye.

For closer objects, u is smaller and hence f should be smaller. The smaller distance at which a person can clearly see, is the minimum possible focal length f, for which ciliary muscles are most strained.

The closest distance for clear vision:

\frac{1}{{{u_{\min }}}}\, = \,\frac{1}{{{f_{\min }}}}\,\, - \,\,\frac{1}{{\rm{v}}}

For an average grown – up person, {u_{\min }}should be around 25 cm or less. Thus, for a normal eye, distance of the near point should be around 25 cm or less and the far should be at infinity.

(1) Myopia or Near sightedness:

A person suffering from this defect cannot see distance objects clearly because {f_{\max }}is less than the distance from the lens to the retina. The parallel beam coming from the distance object focus short of the retina.


Cause: The lens is too thick or the diameter of the eyeball is larger than usual.

Remedy: The rays should be made a bit divergent before entering the eye so that they focus a little later.

Power of lens needed: Suppose, a person can see an object at a maximum distance x. Thus with fully relaxed muscles, rays coming from the distance x converge on the retina. If the eye is to see a distance object clearly, the diverging lens should form the virtual image of the distant object at a distance x.

\frac{1}{f}\, = \,\frac{1}{{\rm{v}}}\, - \,\frac{1}{u}

Put {\rm{v}}\,{\rm{ = }}\, - x\,\,\,\,\,and\,\,\,\,\,u\, = \, - \infty

\therefore \,\,\,\,\,\,\frac{1}{f}\,\, = \,\, - \frac{1}{x}\,\, - \,\,\frac{1}{{\left( { - \infty } \right)}}

P\, = \,\frac{1}{f}\, = \,\frac{{ - 1}}{x}

(2) Hyper metropia or far sightedness:

A person suffering from this defect cannot clearly see objects close to the eye.


Cause: The eye – lens is too thin at the center and/ or the eyeball is shorter than normal, So that they focussed the incoming light at a point behind the retina.

Remedy: A convergent lens is needed to compensate the defect.

Power of a lens needed: Let the eye can clearly see an object at a minimum distance Y. If the eye see clearly an object at 25 cm, the converging lens should form an image of this object at a distance Y.

Hereu\, = \, - 25, {\rm{v}}\,{\rm{ = }}\,{\rm{ - Y}}

\frac{1}{{\rm{v}}}\, - \,\frac{1}{u}\, = \,\frac{1}{f}\\
 - \frac{1}{Y}\, + \,\frac{1}{{25}}\, = \,\frac{1}{f}\\
P\, = \,\frac{1}{f}\, = \,\frac{1}{{25}}\,\, - \,\,\frac{1}{Y}

(3) Astigmatism:

This occurs when the cornea is not spherical in shape e.g the cornea could have a larger curvature in vertical plane than in horizontal plane or vice – versa. Such a person cannot see all the directions equally well. A particular direction in a plane perpendicular to the line of sight is most visible while direction perpendicular to this is least visible.

Remedy: Glasses with different curvatures in different planes are used to compensate for the deshaping of the eye lens. Optician call them cylindrical glasses.

This defect can occur along with myopia or hypermetropia.


Note: In old age, a person may develop myopia and hypermetropia then he need a converging glass for reading purpose and a diverging glass for seeing at a distance.

Such person either keep two sets of spectacles or a spectacle with upper portion divergent and lower portion convergent (bifocal).

Post Author: E-Physics

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