A spherical glass is attached to a rigid wall as shown in the figure. An observer located at point \(\mathrm{O}\) is looking at a point \(\mathrm{A}\) on the wall. The refractive index of the glass is 1.5 and that of air is 1.0. The distances are \(\mathrm{OA}=8 \mathrm{~cm}, \mathrm{XA}=3\) \(\mathrm{cm}\). If the radius of curvature of spherical glass surface is \(R\) \(=5 \mathrm{~cm}\), then the apparent distance of \(\mathrm{A}\) from observer \(\mathrm{O}\) 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.