Which of the following measurements requires ‘index correction’?

Solution & Explanation

‘Index correction’ removes the error caused by the gap between the position of an optical element (the lens/mirror) and the index mark or pin tip read off on the optical-bench scale. The pole/optical centre of a lens does not sit exactly at the scale reading of its holder, and a pin tip is not exactly at its stand’s mark, so each separation read on the bench carries a fixed offset. This offset is found beforehand and added/subtracted as the index correction. Therefore it applies to the focal-length-of-lenses experiment on an optical bench. The other options use different corrections: meter bridge → end corrections; simple pendulum → none of this type; resonance tube → end correction (≈0.3d), not index correction. Hence the answer is option C, measurement of focal length of lenses using an optical bench.