Question

An object is placed first at infinity and then at $20cm$ from the object-side focal plane of a convex lens. The two images thus formed are $5cm$ apart. The focal length of the lens is

• A. $5cm$
• B. $10cm$
• C. $15cm$
• D. $20cm$

Answer 1

The correct option is B $10cm$

The convex mirror formula is,

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

In the first case, the object is placed at infinity, i.e., $u=\infty$. We put this in the mirror formula and get-

$\frac{1}{f}=\frac{1}{v}-\frac{1}{\infty }$

$\Rightarrow f=v$

In the second case, $v=(f+5)\text{cm}$ and $u=-(f+20)\text{cm}$. So we put these in the mirror formula and get-

$\frac{1}{f}=\frac{1}{f+5}-\frac{1}{-(f+20)}$

$\frac{1}{f}=\frac{1}{f+5}+\frac{1}{(f+20)}$

$\frac{1}{f}=\frac{f+20+f+5}{(f+5)(f+20)}$

$\frac{1}{f}=\frac{2f+25}{(f+5)(f+20)}$

$2f^2+25f=f^2+25f+100$

$f^2=100$

$\therefore f=10\text{cm}$

So, option (B) is correct.