In an experiment to measure the focal length ( \(f\) ) of a convex lens, the magnitude of object distance \((x)\) and the image distance \((y)\) are measured with reference to the focal point of the lens. The \(y-x\) plot is shown in figure. The focal length of the lens is _______ \(\mathrm{cm}\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.