Правка раздела «Statement»
en/13.1.15.md
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| ### Statement | |||
| − | $13.1. | ||
| + | $13.1.5.$ 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 | |||
| $f = 36\;\rm{cm}$ | |||
| ещё строк без изменений 13 | |||
| @@ -1,6 +1,6 @@ | |||
| ### Statement | ### Statement | ||
| $13.1. |
$13.1.5.$ 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 | ### Solution | ||
| If image is enlarged by one and a half times,\ | If image is enlarged by one and a half times,\ | ||
| $k = \frac{s'}{s}$ (1)\ | $k = \frac{s'}{s}$ (1)\ | ||
| where $k$ = 1.5 is the magnification of the image, $s$ is the object-mirror distance and $s'$ is the image-mirror distance.\ | 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,\ | It's known that,\ | ||
| $\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}$ (2)\ | $\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}$ (2)\ | ||
| From (1),\ | From (1),\ | ||
| $s' = ks$ (3)\ | $s' = ks$ (3)\ | ||
| Putting (3) into (2):\ | Putting (3) into (2):\ | ||
| $f = \frac{ks}{k+1} = 36\;\rm{cm}$ | $f = \frac{ks}{k+1} = 36\;\rm{cm}$ | ||
| #### Answer | #### Answer | ||
| $f = 36\;\rm{cm}$ | $f = 36\;\rm{cm}$ | ||
| ещё строк без изменений 13 | |||