Question

What is the magnifying power of convex lens of power 40 diopter when used as a magnifying glass?

Answer 1

Question

What is the magnifying power of convex lens of power 40 diopter when used as a magnifying glass?

Answer

By definition, optical power $D = 40$ dioptre $= \frac{1}{F}$, where $F$ is a focal length of the lens.

Thin lens equation:

$$D = \frac{1}{F} = \frac{1}{a} + \frac{1}{b},$$

where $a = OA$ is the distance from the lens to the object and $b = OB$ is the distance from the lens to the image.

Fig. 1. Scheme of convex lens

The magnification is

$$m = \frac{BB'}{AA'} = \frac{OB}{OA} = \frac{b}{a},$$

where we use similarity of triangles $OAA'$ and $OBB'$. Multiplying the first equation by $a$ we obtain

$$aD = 1 + \frac{a}{b} \Rightarrow \frac{b}{a} = \frac{1}{aD - 1}.$$

Thus, the magnification of lens is

$$m = \frac{1}{aD - 1}.$$

For the final answer we need to know the distance $a$ between lens and object.