Question

What should be the value of distance $d$ so that the final image is formed on the object itself ? (Focal lengths of the lenses are as given in the figure).

• A. $10\text{cm}$
• B. $20\text{cm}$
• C. $5\text{cm}$
• D. None of these

Answer 1

The correct option is A $10\text{cm}$

For the convex lens, using lens formula,

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

$\Rightarrow \frac{1}{v}-\frac{1}{(-10)}=\frac{1}{10}$

$\Rightarrow \frac{1}{v}=0\Rightarrow v=\infty$

Now, for the concave lens, using lens formula,

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

$\frac{1}{v^{\prime }}-\frac{1}{\left(\infty \right)}=\frac{1}{-20}$

$\Rightarrow v^{\prime }=-20\text{cm}$


Hence, to form the final image on the object itself, the distance $d$ should be $10\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.