JEE Main 2023 — Mathematics in Physics Question with Solution

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 $5.25 \mathrm{mm}$ and apparent thickness of the glass slab at $5.00 \mathrm{mm}$. Travelling microscope has $20$ divisions in one $\mathrm{cm}$ 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 ______