Question

Which of the following options is correct?

$f_o$ is the focal length of the objective lens and $f_e$ is the focal length of the eyepiece of a compound microscope.

• A. The magnification depends only on $f_o$.
• B. The magnification depends only on $f_e$.
• C. The magnification depends on both $f_o$ and $f_e$.
• D. The magnification is independent of focal lengths of both objective lens and eyepiece.

Answer 1

The correct option is C The magnification depends on both $f_o$ and $f_e$.

We know that,

$\left(i\right)$ Magnification of the compound microscope when the final image is formed at the least distance of distinct vision is given by,

$m=\frac{v_o}{|u_o|}(1+\frac{D}{f_e})$

$\left(ii\right)$ Magnification of the compound microscope when the final image is formed at the infinity is given by,

$m=\frac{v_o}{|u_o|}\left(\frac{D}{f_e}\right)$

So, from $\left(i\right)$ and $\left(ii\right)$, we can see that, magnification depends on $\frac{1}{f_e}$.

Also, from lens formula, $\frac{1-\frac{v_o}{u_o}}{v_o}=\frac{1}{f_o}$

So, $\frac{v_o}{u_o}$ depends on $\frac{1}{f_o}$.

Thus, again from $\left(i\right)$ and $\left(ii\right)$, magnification depends on $\frac{1}{f_o}$.

Therefore, the magnification depends on both $f_o$ and $f_e$.

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