Question

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 $5.25mm$ and apparent thickness of the glass slab at $5.00mm$. 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

Answer 1

Answer: 41

$u=\frac{h}{h^{\prime }}=\frac{5.25}{5.00}$
Least count $=\frac{1}{20}cm-\frac{49}{50}\cdot \frac{1}{20}cm$
$=\frac{1}{50}\times \frac{1}{20}cm=0.01mm$
$\ln u=\ln h-\ln h^{\prime }$
$\frac{du}{u}=\frac{dh}{h}-\frac{dh{}^{\prime }}{h^{\prime }}$
$du=\left[\frac{0.01}{5.25}+\frac{0.01}{5.00}\right]\frac{5.25}{5.00}$
$=\frac{41}{10}\times 10^{-3}$
$=41$