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The visual angle is maximum for unaided eye, when the object is placed at near point.


{\theta _0}\, = \,\frac{h}{D}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.............\,\left( 1 \right)

h – Size of the object.

D – The least distance for clear vision.

This angle can be further increased, if a converging lens of short focal length is placed just in front of the eye. Here, lens acts as a simple microscope or a magnifier.

CASE 1: When final image is at infinity – i.e normal adjustment.

When an object is at first focal point ‘F’ of a convex lens, then its image will formed at infinity. The angle subtended on the lens (and hence on the eye) is

\theta \,\, = \,\frac{h}{D}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...................\,\left( 2 \right)\,

Here f\, < \,D

\therefore \,\,\,\,\,\theta \,\, > \,\,{\theta _o}


The ciliary muscles are least strained under normal adjustment.

Magnifying power:

The magnifying power is the factor by which the image on the retina can be enlarged by using the microscope.

M\, = \,\,\frac{\theta }{{{\theta _0}}}\,\, = \,\,\frac{{h/f}}{{h/D}}\,\, = \,\,\frac{D}{f}

If f\, < \,\,D, then M\,\, > \,\,1

CASE 2: When final image is at near point.

When object is placed within its first focal plane, then virtual erect magnified image is formed at near point i.e 25 cm. The eye is strained but magnifying power is more.


M\, = \,\frac{\theta }{{{\theta _0}}}\, = \,\frac{{h/u}}{{h/D}}\,

M = \,\,\,\frac{D}{u}

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

Put u\, = \, - {\rm{v}}

\begin{array}{l} {\rm{v}}\,\,{\rm{ = }}\,\,{\rm{ - }}\,{\rm{D}}\\ f\,\, = \,\,f\\ \frac{1}{{ - D}}\,\, + \,\,\frac{1}{u}\,\, = \,\,\frac{1}{f} \end{array}

 - 1\, + \,\,\frac{D}{u}\,\, = \,\,\frac{D}{f}

\frac{D}{u}\, = \,\,1\,\, + \,\,\frac{D}{f}

M\, = \,\,1\,\, + \,\,\frac{D}{f}\,

The lesser is the focal length of the convex lens, greater is the magnifying power. It has a limited maximum magnification m\,\, \le \,\,9.


Jewellers and watch makers make use of this lens to obtain a magnified view of fine jewellery work and the small components of the watches.

On the other hands it is used in science lab to see slides and to read the vernier scales attached to the instruments.