JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2023
- Hard
- Numerical
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 \(..............\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(41\)
Step-by-step Solution
Detailed explanation
\(u =\frac{ h }{ h ^{\prime}}=\frac{5.25}{5.00}\)
Least count \(=\frac{1}{20} cm -\frac{49}{50} \cdot \frac{1}{20} cm\)
\(=\frac{1}{50} \times \frac{1}{20} cm =0.01\,mm\)
\(\ln u =\ln h -\ln h ^{\prime}\)
\(\frac{ du }{ u }=\frac{ dh }{ h }-\frac{ dh ^{\prime}}{ h ^{\prime}}\)
\(du =\left[\frac{0.01}{5.25}+\frac{0.01}{5.00}\right] \frac{5.25}{5.00}\)
\(=\frac{41}{10} \times 10^{-3}\)
Ans. \(=41\)
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