A compound microscope has fₒ = 1 cm and fₑ = 5 cm. Its total angular magnification magnitude is 90 with final image at the near point D = 25 cm. Exact lens separation is:
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A compound microscope has fₒ = 1 cm and fₑ = 5 cm. Its total angular magnification magnitude is 90 with final image at the near point D = 25 cm. Exact lens separation is:

G1 Physics · Accepted Answer

GIVEN: Compound microscope fₒ = 1 cm, fₑ = 5 cm; near point D = 25 cm; total angular magnification magnitude 90. Step 1: Near-point eyepiece magnification mₑ = 1 + D/fₑ = 1 + 25/5 = 6. Step 2: Objective linear magnification magnitude |mₒ| = |M|/mₑ = 90/6 = 15. Step 3: Objective real-image distance vₒ from |mₒ| = vₒ/fₒ - 1: 15 = vₒ/1 - 1 ⇒ vₒ = 16 cm. Step 4: Eyepiece object distance s = fₑD/(fₑ + D) = 5 × 25/(5 + 25) = 25/6 cm. Step 5: Exact tube length L = vₒ + s = 16 + 25/6 = (96 + 25)/6 = 12…