Question

An object is placed at a distance of $10\, cm$ from co-axial combination of two lenses $A$ and $B$ contact. The combination forms a real image three times the size of the object. If lens $B$ concave with a focal length of $30\,cm$. The nature and focal length of lens $A$ is

• A. convex, 12 cm
• B. concave, 12 cm
• C. convex, 6 cm
• D. convex, 18 cm

Answer 1

Answer: (C)

Magnification $m=\frac{v}{-u}=-3 v =3 u =30\, cm$
Focal length of co-axial combination
$\frac{1}{f_{1}}+\frac{1}{f_{2}}=\frac{1}{v}-\frac{1}{u}$
$-\frac{1}{30}+\frac{1}{f_{2}}=\frac{1}{30}+\frac{1}{10}$
$=\frac{4}{30} \frac{1}{f_{2}}=\frac{4+1}{30}=\frac{5}{30}$
$f_{2}=\frac{30}{5}=6\, cm$
Hence, lens $A$ is convex lens.