Question

A convex mirror of focal length f and a convex lens of focal length f / 2 are placed at a distance 2 f apart. The final image is formed at the middle of lens and mirror. Find the distance of object from lens:

Answer 1

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 = \(\frac{f}{2}\)