Geomertical optics- derivation of graph of (u+v) against u

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Homework Help Overview

The discussion revolves around deriving the shape of a graph representing the relationship between the sum of object distance (u) and image distance (v) in geometrical optics, specifically in the context of the lens formula. The original poster seeks clarification on how to identify the minimum points of the graph, as provided in their textbook without explanation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the lens formula \( \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \) as a starting point. There are inquiries about rearranging this equation to express v in terms of u and f. The original poster expresses confusion regarding the derivation of the graph's shape and the minimum points.

Discussion Status

The conversation is ongoing, with participants exploring the relationships between u, v, and f. Some guidance has been offered regarding the lens formula and rearranging it to find v, but there is no consensus or clear resolution yet.

Contextual Notes

The original poster indicates a lack of understanding of the derivation process as presented in their textbook, which may imply constraints on the information available to them. They are specifically looking for clarification on the graph's shape and minimum points.

somecelxis
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Homework Statement



may i know how to derive the the sha[pe of graph and get the point of min (2f , 4f) ? i really have no idea how to get the shape of the graph and the min point. The book give it without any explanation.

Homework Equations





The Attempt at a Solution

 

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Do you have an equation that related u,v, and f?
Put v=d-u, and solve for d.
 
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Simon Bridge said:
Do you have an equation that related u,v, and f?
Put v=d-u, and solve for d.

what equation is that? v=d-u i have only 1/u +1/v =1/f in my book
 
1/u + 1/v = 1/f is a good place to start - that's the lensmakers formula.

can you rearrange that equation to make v the subject?
 
v= uf /(u-f) what shall i do next?
 
somecelxis said:
v= uf /(u-f) what shall i do next?
OK - so if that is v, then v+u = ?
 

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