Solving for p: Finding Distance from Convex Lens

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Homework Help Overview

The discussion revolves around finding the distance of an object from a convex lens, denoted as p, given the total distance between the object and its image (p + q) and the relationship between object distance, image distance, and focal length.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of the relationship between p, q, and the focal length, questioning how to isolate p with limited information. There is discussion about the significance of the image size being half that of the object and its relation to similar triangles.

Discussion Status

The discussion is active, with participants offering insights into potential relationships between the distances and the image size. Some guidance has been provided regarding the use of similar triangles and height relationships, but no consensus has been reached on a definitive method to find p.

Contextual Notes

Participants note the lack of specific values for q and f, which are critical for solving the problem. The assumption that the image is smaller than the object is also under examination.

Nano
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Homework Statement


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?


Homework Equations


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


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.
 
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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?
 
It said if was 1/2 the size of the original. But how does that information help?
 
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?
 
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.
 
Ok, thank you for your help!
 

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