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

AI Thread Summary
To derive the graph of (u+v) against u, start with the lensmaker's formula: 1/u + 1/v = 1/f. Rearranging this gives v = uf/(u-f). The next step involves substituting this expression for v into (u+v) to analyze its behavior. The minimum points of the graph occur at specific values, notably at 2f and 4f. Understanding these relationships is crucial for visualizing the graph's shape and identifying the minimum points.
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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.

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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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