Question

A convex lens of focal length $10\text{cm}$ in contact with a concave lens of focal length $20\text{cm}$. This combination is used to focus an object positioned $30\text{cm}$ infront of combination. The image will be formed at a distance of

• A. $30\text{cm}$
• B. $40\text{cm}$
• C. $50\text{cm}$
• D. $60\text{cm}$

Answer 1

The correct option is D $60\text{cm}$

Given, $f_1=10\text{cm}{f}_2=-20\text{cm}$

We know, $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{10}-\frac{1}{20}=\frac{2-1}{20}=\frac{1}{20}$

Equivalent focal length $F=20\text{cm}$
Given, $u=-30\text{cm}$

Using lens formula, $\frac{1}{F}=\frac{1}{v}-\frac{1}{u}$

$\Rightarrow \frac{1}{20}=\frac{1}{v}+\frac{1}{30}$

$\Rightarrow \frac{1}{20}-\frac{1}{30}=\frac{1}{v}$

$\Rightarrow \frac{3-2}{60}=\frac{1}{v}$

$\Rightarrow v=60\text{cm}$