For lens,
v = 2f + \(\frac{f}{2}\)
v = \(\frac{5f}{2}\)
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)
\(\frac{1}{(5f/2)}\)\(-\frac{1}{u}=\frac{1}{(f/2)}\)
\(\frac{1}{u}\) = \(\frac{2}{5f}\) - \(\frac{2}{f}\)
\(\frac{1}{u}\) = \(\frac{2-10}{5f}\)
\(\frac{1}{u}\) = \(\frac{-8}{5f}\)
u = \(\frac{-5f}{8}\)
|u| = \(\frac{5f}{8}\)
For convex mirror,
\(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\)
(∵ v = -f)
\(\frac{-1}{f}+\frac{1}{u}=\frac{1}{f}\)
\(\frac{1}{u}=\frac{1}{f}+\frac{1}{f}\)
\(\frac{1}{u}=\frac{2}{f}\)
u = \(\frac{f}{2}\)