Question

A convex lens of focal length $15cm$ is spilt into two halves and the two halves are placed at a separation of $120cm$. Between the two halves of convex lens a plane mirror is placed horizontally and at a distance of $4mm$ below the principal axis of the lens halves. An object $AB$ of length $2mm$ is placed at a distance of $20cm$ from one half lens as shown in the figure. The final image of the point $A$ is formed at a distance of $\frac{n}{3}mm$ from the principal axis. Determine the value of $n$.

Answer 1

8
The first half-lens forms the image $AB(=6mm).$
$\therefore \frac{1}{v}-\frac{1}{-20}=\frac{1}{15}v=+60cm$.
$\therefore m_1=-3$.
The plane mirror forms the image $AB$ with $A$ located $8mm$ below the principal axis. The second half lens forms the image $AB"$. Now $u=-60cm$
$\Rightarrow v=+20cm$
$\therefore m_2=-\frac{1}{3}$
$\therefore A$ is located at $\frac{8}{3}mm$ above the principal axis.
$\therefore n=8$