Question
Define the magnifying power of a compound microscope when the final image is formed at infinity. Why must both the objective and the eyepiece of a compound microscope has short focal lengths? Explain.
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Answer
When the final image is formed at infinity.
When the final image is formed at infinity, the angular magnification due to the eyepiece is
$\text{m}_e=D/\text{f}_e$
Thus, the total magnification when the image is formed at infinity can be defined as the product of magnification of objective lens and eyepiece. i.e
$m=m_0 m_e=\left(L / f_0\right)\left(D / f_e\right)$
From the above the equation, we can see that to achieve a large magnification of a small object, the objective and eyepiece should have small focal lengths.
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