A compound microscope uses two symmetric biconvex lenses as objective and eyepiece. The objective lens is cut by a plane perpendicular to its principal axis, producing two identical plano-convex lenses, and one of these halves is used as the new objective. If the object distance is kept unchanged, how should the tube length be changed to retain the same magnifying power?
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Question

A compound microscope uses two symmetric biconvex lenses as objective and eyepiece. The objective lens is cut by a plane perpendicular to its principal axis, producing two identical plano-convex lenses, and one of these halves is used as the new objective. If the object distance is kept unchanged, how should the tube length be changed to retain the same magnifying power?

Options

G1 Physics · Accepted Answer

For a compound microscope in normal adjustment, the magnifying power is proportional to M ∝ L ÷ f₀, when the eyepiece and viewing condition are unchanged. For the original symmetric biconvex objective, 1 ÷ f₀ = (μ-1)(2 ÷ R). After cutting it into a plano-convex lens, 1 ÷ f'₀ = (μ-1)(1 ÷ R) = 1 ÷ (2f₀). Therefore, f'₀ = 2f₀. To keep L ÷ f₀ unchanged, the new tube length must satisfy L' ÷ (2f₀) = L ÷ f₀. Hence, L' = 2L. Correct option: A.