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  • 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 <img alt="5.25 \mathrm{~mm}" sr

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 as 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 __________.

Option: 1

41


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \mu=\frac{h}{h^1}=\frac{\text { Real depth }}{\text { Apparent depth }} \\ & \text { Least Count }=\text { M.S.D. }- \text { V.S.D } \\ & =\text { M.S.D. }-\frac{49}{50} \text { M.S.D } \\ & =\left(\frac{50-49}{50}\right) \text { M.S.D } \\ & =\frac{1}{50} \text { M.S.D } \\ & =\frac{1}{50} \times \frac{1}{20} \mathrm{~cm} \\ & =\frac{1}{1000} \mathrm{~cm} \\ & =\frac{10}{1000} \mathrm{~mm}=0.01 \mathrm{~mm} \end{aligned}

\begin{aligned} & \operatorname{In} \mu=\operatorname{lnh}-\operatorname{lnh}{ }^{\prime} \\ & \frac{\mathrm{d} \mu}{\mu}=\frac{\mathrm{dh}}{\mathrm{h}}+\frac{\mathrm{dh} \mathrm{h}^{\prime}}{\mathrm{h}^{\prime}} \\ & \mathrm{d} \mu=\mu\left[\frac{\mathrm{dh}}{\mathrm{h}}+\frac{\mathrm{dh}^{\prime}}{\mathrm{h}^{\prime}}\right] \\ & \mathrm{d} \mu=\mu\left[\frac{\mathrm{dh}}{\mathrm{h}}+\frac{\mathrm{dh}^{\prime}}{\mathrm{h}}\right]=\frac{5.25}{5.00}\left[\frac{0.01}{5.25}+\frac{0.01}{5.00}\right] \\ & \left.=\frac{41}{10} \times 10^{-3}\right] \end{aligned}

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Ritika Kankaria

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