Question

If a lens is moved towards the object from a distance of $20cm$ to $15cm$, the magnification of the image remains the same. The focal length of the lens is

• A. 18.2 cm
• B. 16.8 cm
• C. 17.5 cm
• D. 15.5 cm

Answer 1

Answer: (C)

From lens formula
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
where $f$ is focal length, $v$ the image distance and $u$ the object distance.
For convex lens
$\frac{1}{f}=\frac{1}{v}-\frac{1}{(-u)}=\frac{1}{v}+\frac{1}{u}$
Multiplying both sides by, $u$ we get
$\frac{u}{v}+1=\frac{u}{f}$
$\Rightarrow \frac{u}{v}=\frac{u-f}{f}$
or $\frac{v}{u}=\frac{f}{u-f}$
or $m=\frac{f}{u-f}$
According to question
$m_1=-m_2$
$\therefore \frac{f}{u_1-f}=\frac{f}{f-u_2}$
$\Rightarrow \frac{f}{20-f}=\frac{f}{f-15}$
$\Rightarrow 2f=20+15$
$\Rightarrow f=\frac{35}{2}=17.5cm$