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Luisito правка от 11 июн. 2026 г., 21:46

правка #18662 позже →

en/13.1.15.md +29 −0

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		+	### Statement
		+
		+	$13.1.5.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	### Statement
		+
		+	$13.1.15.$ The object is located on the main optical axis of the concave mirror at a distance of 60 cm from the mirror pole. Determine the focal length of the mirror, if the image of the subject is valid and enlarged by one and a half times.
		+
		+	### Solution
		+
		+	If image is enlarged by one and a half times,\
		+	$k = \frac{s'}{s}$ (1)\
		+	where $k$ = 1.5 is the magnification of the image, $s$ is the object-mirror distance and $s'$ is the image-mirror distance.\
		+	It's known that,\
		+	$\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}$ (2)\
		+	From (1),\
		+	$s' = ks$ (3)\
		+	Putting (3) into (2):\
		+	$f = \frac{ks}{k+1} = 36\;\rm{cm}$
		+
		+	#### Answer
		+
		+	$f = 36\;\rm{cm}$
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$13.1.5.$ [Insert the problem statement]

			### Solution

			### Statement

			$13.1.15.$ The object is located on the main optical axis of the concave mirror at a distance of 60 cm from the mirror pole. Determine the focal length of the mirror, if the image of the subject is valid and enlarged by one and a half times.

			### Solution

			If image is enlarged by one and a half times,\
			$k = \frac{s'}{s}$ (1)\
			where $k$ = 1.5 is the magnification of the image, $s$ is the object-mirror distance and $s'$ is the image-mirror distance.\
			It's known that,\
			$\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}$ (2)\
			From (1),\
			$s' = ks$ (3)\
			Putting (3) into (2):\
			$f = \frac{ks}{k+1} = 36\;\rm{cm}$

			#### Answer

			$f = 36\;\rm{cm}$

			#### Answer

			[Insert a concise answer or boxed result]