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 $5.25 \,mm$ 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

Answer 1

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