Question

Two thin converging lenses are placed on a common axis, so that the focus of the second lens coincides with the optic center of the first lens. An object is placed as shown. Find the lateral maginification of the system of lenses

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $-\frac{1}{2}$


The image formed by first lens $I_1$ will be at a distance $2f$ with lateral magnifcation $m_1=-1$.

For the second lens, this image will behave as a virtual object.

Using the lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$, we have,

$\frac{1}{v}-\frac{1}{f}=\frac{1}{f}\Rightarrow v=\frac{f}{2}$

$\therefore m_2=\frac{v_2}{u_2}=\frac{\left(\frac{f}{2}\right)}{f}=\frac{1}{2}$

Hence, final image is formed at a distance $\frac{f}{2}$ from the second lens.

Total lateral magnification, $m=m_1\times m_2=(-1)\times \left(\frac{1}{2}\right)=-\frac{1}{2}$

Hence, option (b) is the correct answer.