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First time I've experienced a real problem rearding equations in physics, so:

As conclusions to the lab on focal points and and center of curvatures (which will be explained at a later date), we were given the following relationships:

So = Do - f

Si = Di - f

And, we were ably to verify the Gaussian? form of the equation through a series of experiments:

1/Do + 1/Di = 1/f

And yadayada, now the final conclusion for the lab simply asks for a relationship between f, So, and Si that can be expressed analytically, graphically, and verbally.

After wrecking my brain on this question, I eventually checked the following site: http://www.sasked.gov.sk.ca/docs/physics/u3b32phy.html [Broken] to find this relationship:

SoSi = f^2

However, I obviously cannot go that far, lol. Here is, as best as I can transcribe, how far I got:

So = do -f ----> do = So + f

Si = di -f ----> di = Si + f

then, I substituted those into the equation, getting this stuff:

1/(So +f) - 1/(Si + f) = 1/f

I know for sure (I think, well w/e) that that is the first correct step. After that, I tried a couple of different things, the most prominent being the LCM/LCD approach:

(Si + f) - (So + f)

all over or divided by

(So + f)(Si + f)

all equals = 1/f

then....some simplification:

Si - So

all over or divided by

(So + f)(Si + f)

all equals = 1/f

from there, a smart guy at school (whose done some college level physics...I thinK) told me I could flip the numerator/denominator in both sides of the equation...giving....

(Si + f)(So + f)

all over or divided by

Si - So

all equals = f

(I just put (si + f) in the front b/c it looks a bit better I think)

However, after this we were both rather clueless as to how further simplify the expression...I tried expanding the numerator:

SiSo + Sif + Sof + f^2

all over or divided by

Si - So

all equals = f

but, like, then what? Si, So, f...nothing is common in the numerator anyhow. Eventually I got kinda berserk and tried taking out a Si and an f from the numerator...not pretty:

(Si)(So + f) + (f)(So + f)

all over or divided by

Si - SO

all equals = f

yawn..now what?....mm then this:

(So + f)(Si + f)

all over or divided by

Si - So

all equals = f

and that last part, I'm not even sure about my algebra lol. so yeah, I'm sorta hopeless, and I can't find much besides the aformentioned site for the derviation of this formula, but I think I'm on the right track so if anyone has any ideas...go ahead.

--Zeros

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# Mirror Equations: Derivation of Newtonian Form

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