Q37. A compound microscope has tube length 20 cm and objective linear magnification magnitude 9 in normal adjustment. If the eyepiece focal length is 3 cm, the objective focal length is:
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Question

Q37. A compound microscope has tube length 20 cm and objective linear magnification magnitude 9 in normal adjustment. If the eyepiece focal length is 3 cm, the objective focal length is:

G1 Physics · Accepted Answer

GIVEN: Compound microscope L = 20 cm, eyepiece fₑ = 3 cm, objective magnification magnitude |mₒ| = 9; final image at ∞. Step 1: Objective intermediate-image distance vₒ = L − fₑ = 20 − 3 = 17 cm. Step 2: Exact objective magnification relation |mₒ| = vₒ/fₒ − 1. Step 3: Substitute: 9 = 17/fₒ − 1 ⇒ 10 = 17/fₒ. Step 4: fₒ = 17/10 = 1.7 cm. FINAL ANSWER: Objective focal length = 1.7 cm. Option C.