The graph shows the variation of the magnification (m) produced by a thin lens with image distance (v). The focal length of the lens is:
Show Hint
To solve questions involving lenses and magnification, remember to use the lens formula and the relationships between magnification and object/image distances.
The given graph shows the relationship between magnification \(m\) and image distance \(v\). From the graph, we observe that the magnification \(m\) is related to \(v\) in a manner that can be interpreted in terms of the lens formula:
\[
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
\]
Where \(f\) is the focal length of the lens, \(v\) is the image distance, and \(u\) is the object distance. Using the given relationship between \(m\) and \(v\) from the graph, and analyzing the geometry and algebra behind the graph, we can deduce that the focal length of the lens is given by:
\[
f = \frac{b^2}{ac}
\]
Thus, the correct answer is \(\frac{b^2}{ac}\).
