In an experiment a convex lens of focal length $15 c m$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5 c m$ from it. It is found that an object and its image coincide, if the object is placed at a distance of $20 c m$ from the lens. The focal length of the convex mirror is:

Question

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Answer 1

for convex lens:
$u = - 20 c m, f = 15 c m$
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
$\frac{1}{v} = \frac{1}{1 5} + (\frac{1}{- 2 0})$
$v = \frac{- 1 5 \times 2 0}{- 2 0 + 1 5} = \frac{3 0 0}{5} = 60 c m$
for mirror:
$u = 55 c m, f = ?$
for the mirror to form image at '0':
$u = R = 2 f$
$f = \frac{R}{2} = 27.5 c m$

Answer 2

for convex lens:

u = - 20 c m, f = 15 c m

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

\frac{1}{v} = \frac{1}{f} + \frac{1}{u}

\frac{1}{v} = \frac{1}{1 5} + (\frac{1}{- 2 0})

v = \frac{- 1 5 \times 2 0}{- 2 0 + 1 5} = \frac{3 0 0}{5} = 60 c m

for mirror:

u = 55 c m, f = ?

for the mirror to form image at '0':

u = R = 2 f

f = \frac{R}{2} = 27.5 c m