Новое решение

Valter правка от 20 авг. 2026 г., 18:57

правка #20176 позже →

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		+	### Statement
		+
		+	$13.3.15.$ [Insert the problem statement]
		+
		+	### 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 ($\Gamma = 10$):
		+	$$F = \frac{25 \text{ cm}}{10} = 2.5 \text{ cm}$$
		+
		+	#### Answer
		+	$F = 2.5 \text{ cm}$
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$13.3.15.$ [Insert the problem statement]

			### 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 ($\Gamma = 10$):
			$$F = \frac{25 \text{ cm}}{10} = 2.5 \text{ cm}$$

			#### Answer
			$F = 2.5 \text{ cm}$

			#### Answer

			[Insert a concise answer or boxed result]