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

[somecelxis]

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

 

[Simon Bridge]

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

 

[somecelxis]

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

 

[Simon Bridge]

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?

 

[somecelxis]

v= uf /(u-f) what shall i do next?

 

[Simon Bridge]

v= uf /(u-f) what shall i do next?

OK - so if that is v, then v+u = ?