Optics question, locate mirror and its focal length

AI Thread Summary
The problem involves a 10 cm tall object placed at the zero mark of a meter stick, producing an upright, 4 cm tall image at the 42 cm mark, indicating the use of a convex mirror. The mirror's location can be determined using the mirror formula 1/do + 1/di = 1/f, where do is the object distance and di is the image distance. The object distance is 0 cm, while the image distance is -42 cm (since the image is virtual). The focal length can be calculated from the derived distances, confirming the mirror's convex nature. The solution requires careful ray diagram analysis to pinpoint the mirror's exact location and focal length.
SlothNast
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Homework Statement



"An object 10 cm tall is placed at the zero mark of a meter stick. A spherical mirror located at some point on the meter stick creates an image of the object that is upright, 4 cm tall, and located at the 42 cm mark of the meter stick. Where is the mirror located and what is the focal length?"

Homework Equations



1/do + 1/di = 1/f

The Attempt at a Solution


 
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What have you done so far?
 
Well I've determined it must be a convex mirror, for the upright and miniature image. I have drawn a few rays from the real 10 cm object to the 4 cm image, but I am not sure how to find the location of the mirror and its focal point from that.
 
What rays in particular have you tried? Just two rays is enough.
 

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