An optical bench uses a 10 cm needle to estimate bench errors. Initial readings are x₀=1.1 cm, xᵢ=21.0 cm and xₗ=10.9 cm. For a later lens experiment x₀=0.6 cm, xᵢ=22.5 cm and xₗ=11.4 cm. Which focal length (including bench correction) is obtained?
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Question

An optical bench uses a 10 cm needle to estimate bench errors. Initial readings are x₀=1.1 cm, xᵢ=21.0 cm and xₗ=10.9 cm. For a later lens experiment x₀=0.6 cm, xᵢ=22.5 cm and xₗ=11.4 cm. Which focal length (including bench correction) is obtained?

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G1 Physics · Accepted Answer

The 10 cm needle provides the holder corrections by comparing the known separation with the bench readings. Apply those corrections to object and image distances, then use f=uv/(u+v). The corrected result is 5.5 cm with about 0.1 cm uncertainty. Correct answer: B.