In an experiment to measure the power of a convex lens, the least...

The power of a lens is given by $P = \dfrac{1}{f}$

Using the lens formula, we can write the power in terms of object distance $u$ and image distance $v$ as:

$P = \dfrac{1}{v} - \dfrac{1}{u}$

Differentiating both sides to find the error in power, we get:

$dP = -\dfrac{dv}{v^2} + \dfrac{du}{u^2}$

To find the maximum permissible error, we take the absolute values of the individual error terms and add them:

$\Delta P = \dfrac{\Delta v}{v^2} + \dfrac{\Delta u}{u^2}$

Answer: $\dfrac{\Delta v}{v^2} + \dfrac{\Delta u}{u^2}$