Let \( u \) and \( v \) be the distances of the object and the image from a lens of focal length \( f \). The correct graphical representation of \( u \) and \( v \) for a convex lens when \( |u| > f \), is:
Show Hint
For a convex lens, the object and image distances follow the lens formula, and the graph between \( u \) and \( v \) will be an inverse curve.
In the context of optics, to find the graphical relationship between the object distance (\(u\)) and the image distance (\(v\)) for a convex lens with focal length (\(f\)), we employ the lens formula, which states:
\(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)
This equation rearranges to:
\(uv = f(v+u)\)
or
\(v = \frac{uf}{u-f}\)
Given the requirement \(|u| > f\), it follows that both the object and image distances relate inversely, due to the algebraic form of the equation. The term \((u-f)\) in the denominator ensures that with increasing \(u\), \(v\) does not proportionally increase but rather decreases, highlighting an inverse relationship. This characteristic is depicted graphically as an inverse graph. Therefore, the correct graphical representation of the relationship between \(u\) and \(v\) when \(|u| > f\) for a convex lens is:
