In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as \(5.25\,mm\) and apparent thickness of the glass slab at \(5.00\,mm\). Travelling microscope has \(20\) divisions in one \(cm\) on main scale and \(50\) divisions on Vernier scale is equal to \(49\) divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is \(\frac{x}{10} \times 10^{-3}\), where \(x\) 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.