Question

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

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

Answer 1

The correct option is C convex, $6cm$

Given,

Object distance, $u=10cm$

Real image $\Rightarrow$ other ride $\Rightarrow v=+ve$

Magnification, $m+3\Rightarrow -\frac{v}{u}=3$

So, $v=-3u=-3\times (-10)=30cm$

Combined focal constant $=F$

then $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=\frac{1}{30}-\frac{1}{-10}=\frac{1+3}{30}=\frac{4}{30}$

$\Rightarrow F=\frac{15}{2}cm$

but $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$ so $\frac{2}{15}=\frac{1}{-30}+\frac{1}{f_2}$

Because concave $f_1=-30cm$ on solving we get $\frac{4}{30}+\frac{1}{30}=\frac{1}{f_2}$

$\Rightarrow f_2=6cm+ve\Rightarrow$ convex.