Q13. A microscope has fₒ = 1 cm, fₑ = 5 cm and initially 20 cm separation, with final image at infinity. Without moving the objective or object, the eyepiece is shifted to form the final image at 25 cm. The displacement is:
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Question

Q13. A microscope has fₒ = 1 cm, fₑ = 5 cm and initially 20 cm separation, with final image at infinity. Without moving the objective or object, the eyepiece is shifted to form the final image at 25 cm. The displacement is:

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G1 Physics · Accepted Answer

GIVEN: Eyepiece focal length fₑ = 5 cm; near point D = 25 cm. The objective and object stay fixed. Step 1: In normal adjustment the intermediate image is at the eyepiece focus; required object distance s₁ = fₑ = 5 cm. Step 2: For a final virtual image at D, solve 1/fₑ = −1/D + 1/s₂. Step 3: 1/s₂ = 1/5 + 1/25 = 6/25 ⇒ s₂ = 25/6 = 4.1667 cm. Step 4: Since the intermediate image remains stationary, move the eyepiece closer to the objective by s₁ − s₂. Step 5: Displacement = 5 − 25/6 = 5/6 = 0.8333…