Solution

Statement

$13.3.15.$ The rim of a magnifying glass bears the inscription "$\times 10$", meaning the magnifying glass increases the angular size of the object being viewed by ten times. Determine its focal length.

Solution

The commercial magnification of a magnifying glass, indicated on its rim, is standardly calculated for the case when the eye is accommodated at infinity (a relaxed eye). In this case, the angular magnification $\Gamma$ is determined by the formula:
$$\Gamma = \frac{d_0}{F}$$
where $d_0 = 25 \text{ cm} = 0.25 \text{ m}$ is the distance of most distinct vision for a normal eye, and $F$ is the focal length of the magnifying glass.

Expressing the required focal length $F$ from this formula:
$$F = \frac{d_0}{\Gamma}$$

Substituting the known values ($\Gamma = 10$):
$$F = \frac{25 \text{ cm}}{10} = 2.5 \text{ cm}$$