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(B) The lens formula is given by $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$.In the standard sign convention for a convex lens,the object distance $u$ i

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(B) The lens formula is given by $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$.In the standard sign convention for a convex lens,the object distance $u$ is negative $(-u)$ and the image distance $v$ is positive $(+v)$.Substituting these into the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{-u} = \frac{1}{v} + \frac{1}{u}$.Rearranging for $v$: $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{u-f}{fu}$.Thus,$v = \frac{fu}{u-f}$.As $u$ increases from $f$ to $\infty$,$v$ decreases from $\infty$ to $f$. This represents a rectangular hyperbola in the first quadrant,which corresponds to the graph shown in option $B$.

$A$ student measures the focal length of a convex lens by obtaining an image of an object pin at a distance '$v$' from the lens,with the object placed at a distance '$u$' from the lens. What will the graph between '$u$' and '$v$' look like?

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