Question

A magnifying glass is made of a combination of converging lens of power $ + 20$ dioptres and a diverging lens of power $ - 4$ dioptres. If the least distance of distinct vision is $25\,cm$, the magnifying power is:
A. $3$
B. $4$
C. $5$
D. $7$

Answer 1

Hint:A magnifying glass is a convex lens which is used to create an object's magnified image. Generally, the lens is placed in a box with a handle. A magnifying glass may be used to absorb light, such as to concentrate the radiation of the sun to create a hotspot for fire beginning at the focus.

Complete step by step answer:
Given, Convergent power of a lens,$ = + 20$ dioptres
Divergent power of a lens, $ = - 4$ dioptres
Hence, net power is ${P_{nw}} = 20 - 4 = 16$ dioptres
Least distance, $D = 25\,cm$
Net focal length,
$
{f_{net}} = \dfrac{{100}}{{{P_{net}}}} \\
\Rightarrow{f_{net}} = \dfrac{{100}}{{16}} \\
\Rightarrow{f_{net}} = \dfrac{{25}}{4} \\ $
Hence, the magnification is given by:
$
M = 1 + \dfrac{D}{{{f_{net}}}} \\
\Rightarrow M = 1 + \dfrac{{25}}{{\dfrac{{25}}{4}}} \\
\therefore M = 5 \\ $
Hence, option C is correct.

Additional information:
A magnifying glass magnification depends on where it is located between the eye of the consumer and the object being seen and the overall distance between them. The magnifying power corresponds to the magnification of angles (this should not be confused with optical power, which is a different quantity). The magnifying force is the ratio with and without the lens of the sizes of the images produced on the user's retina.

A converging lens:A convex lens in which at a single point on the opposite side, light rays approaching it parallel to its axis converge. Diverging lens: a concave lens in which light rays bend away (diverge) from its axis which enter it parallel to its axis. By bringing the lens very close to one eye, and shifting the eye and the lens together to achieve the best focus, the greatest magnifying power is obtained. Usually, the object would then still be close to the lens.

Note:Magnifying glasses usually have low magnifying power: $2x - 6x$, with far more common forms of lower-power. At higher magnifications, due to optical aberrations, particularly spherical aberration, the image quality of a simple magnifying glass becomes low. Other forms of hand magnifier are usually used where more magnification or a better picture is needed.