Convex lenses

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1. The problem statement, all variables and given/known data
Given only the distance between the object and its image (p +q), how is it possible to find p, the distance of the object from the convex lens?


2. Relevant equations
1/p + 1/q = 1/f
in this case, p + q =40
also, the image is smaller than the original, so p > 2f


3. The attempt at a solution
I don't understand how to find p if q and f are unknown. I tried solving for q as q=40-p, but that didn't take me anywhere.
 

Delphi51

Homework Helper
3,407
10
You need more information than you gave in part 1.
How did you know the image is smaller than the original - do you know what fraction it is?
 
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It said if was 1/2 the size of the original. But how does that information help?
 
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Ahh, I think I get it. It has something to do with the similar triangles formed by the object/image and a light ray passing through the center of the convex lens, right?
 

Delphi51

Homework Helper
3,407
10
Yes, or you can use the formula relating the object and image heights to their distances from the lens to get a 2nd equation relating p and q.
 
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Ok, thank you for your help!
 

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