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Question

A compound microscope has an objective of focal length \( 2 \, \text{cm} \) and eyepiece of focal
length \( 4 \, \text{cm} \) with a tube length of \( 16 \, \text{cm} \). What is the magnification at
infinity?

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Explanation

**Microscope principle** objective of short focal length forms real image between F_e and 2F_e of eyepiece, eyepiece magnifies to virtual image at D, total magnification product, for f_o=2 cm, f_e=5 cm, L=20 cm, m_o≈10, M_e≈6, M≈60, illustrating high magnification from two stages. Objective magnification: m_o = (L/f_o) = (16/2) = 8 . Eyepiece magnification: m_e = (D/f_e) = (25/4) = 6.25 . Total magnification: m = m_o × m_e = 8 × 6.25 = 50 . Substituting values gives 50, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign conventions and refraction principles.

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