Question

The optical axes of a convex and concave lens are separated by a distance $5\text{mm}$ as shown in the figure. Find the coordinate of the final image formed by the combination if a parallel beam of light is incident on the convex lens. Origin is at the optical centre of the convex lens.

• A. $(25\text{cm},0.5\text{mm})$
• B. $(25\text{cm},-0.5\text{mm})$
• C. $(25\text{cm},2.5\text{mm})$
• D. $(50\text{cm},-2.5\text{mm})$

Answer 1

The correct option is C $(25\text{cm},2.5\text{mm})$

Let $I_1$ and $I_2$ be the first and final images respectively.
Since incident beam is parallel, $I_1$ will be formed at the focus of convex lens.


For concave lens, using lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{-10}=-\frac{1}{10}$$\Rightarrow v=-5\text{cm}$

Since optical axis of concave lens is shifted up by $5\text{mm}$, we can treat $I_1$ as extended object with height $h_o=5\text{mm}$.

$m=\frac{v}{u}=\frac{(-5\text{cm})}{(-10\text{cm})}=\frac{1}{2}=\frac{h_i}{h_o}$
$\Rightarrow h_i=2.5\text{mm}$

Hence, coordinates of final image

$x_{I_2}=30-5=25\text{cm};y_{I_2}=2.5\text{mm}$