Mathematics In Physics Question 4
Question 4 - 29 January - Shift 2
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
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Answer: (41)
Solution:
$u=\frac{h}{h^{\prime}}=\frac{5.25}{5.00}$
Least count $=\frac{1}{20} cm-\frac{49}{50} \cdot \frac{1}{20} cm$
$=\frac{1}{50} \times \frac{1}{20} cm=0.01 mm$
$\ln u=\ln h-\ln h^{\prime}$
$\frac{du}{u}=\frac{dh}{h}-\frac{dh^{\prime}}{h^{\prime}}$
$d u=[\frac{0.01}{5.25}+\frac{0.01}{5.00}] \frac{5.25}{5.00}$
$=\frac{41}{10} \times 10^{-3}$
Ans. $=41$
