Question

An object (O) is placed in front of a concave lens of focal length 20 cm as shown in the figure. Determine the focal length of the convex lens if a real image is formed at a distance of 30 cm by the convex lens.

• A. 15 cm
• B. 30 cm
• C. 45 cm
• D. 60 cm

Answer 1

The correct option is A 15 cm


So, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{30}=\frac{-1}{20}$
$\frac{1}{v}=\frac{-1}{30}-\frac{1}{20}$
$=\frac{-50}{30/20}=\frac{-5}{60}$
$v=-12cm$
Hence for convex lens
$v=30cm$ and $u=-30cm$
Hence the object is at $2f$ as $v=u$
So $2f=30$
$f=15cm$