Lens formula using distances from the focal points

Let the object and image distances measured from the two focal points be $x$ and $y$ respectively.

By Newton’s form of the lens formula, $xy=f^2$

So, the graph of $y$ versus $x$ must satisfy $y=\frac{f^2}{x}$ which is a rectangular hyperbola.

Using the graph

From the given plot, one can read a convenient point on the curve such as $x=10\ \text{cm},\qquad y=40\ \text{cm}$ (equivalently, any other marked point on the same curve gives the same product).

Therefore, $xy = 10\times 40 = 400$

Calculate the focal length

Since $f^2=xy=400$ we get $f=\sqrt{400}=20\ \text{cm}$

Final answer

$\boxed{20}$

Comparison with stored correct answer

Stored correct answer = $20$

This matches the derived answer.