A plano-convex lens made of refractive index 1.5 and having radius of curvature \(\mathrm{R}=4 \mathrm{~cm}\) fits exactly into a plano-concave lens made of refractive index 1.3 and having the same radius of curvature \(\mathrm{R}=4 \mathrm{~cm}\) such that their plane surfaces are parallel to each other. The focal length of the combination is:

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.