Question

An angular magnification of $30\text{X}$ is to be obtained from a compound microscope, having an eyepiece of focal length $5\text{cm}$. Find the magnification produced by the objective lens.

Given angular magnification is achieved in case of the least strain on the eye.

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is A $6$

Given:

$m=30$
$f_e=5\text{cm}$

We know that, in case of the least strain on eye, the final image is formed at infinity.

So, $|u_e|=|f_e|$

Now, magnification due to eyepiece,

$m_e=\frac{D}{|u_e|}=\frac{D}{|f_e|}$

$\Rightarrow m_e=\frac{25}{5}=5$

Further, we know that total magnification by the compound microscope,

$m=m_o\times m_e$

$\Rightarrow 30=m_o\times 5$

$\Rightarrow m_o=6$

Hence, option $\left(A\right)$ is the correct answer.