Q15. A compound microscope has fₒ = 1 cm, fₑ = 5 cm and lens separation 20 cm. For the final image to be at infinity, the magnitude of the object distance from the objective is:
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Q15. A compound microscope has fₒ = 1 cm, fₑ = 5 cm and lens separation 20 cm. For the final image to be at infinity, the magnitude of the object distance from the objective is:

G1 Physics · Accepted Answer

GIVEN: Objective fₒ = 1 cm; eyepiece fₑ = 5 cm; lens separation L = 20 cm; final image at ∞. Step 1: Objective image must lie at eyepiece focus: vₒ = L − fₑ = 20 − 5 = 15 cm. Step 2: Use objective lens formula 1/fₒ = 1/vₒ − 1/uₒ with object on the left, uₒ < 0. Step 3: 1/1 = 1/15 + 1/|uₒ| ⇒ 1/|uₒ| = 1 − 1/15 = 14/15. Step 4: |uₒ| = 15/14 = 1.07143 cm, slightly greater than fₒ as required for a real enlarged image. FINAL ANSWER: 15/14 cm. Option B.