Verified Solution • 2025–26 Session moderate

QJEEM23Ph1b99: JEE Main 2023 Physics - Class 12 JEEM23Ph1b99 Solution: In an experiment of measuring the refractive index of a glass…

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 as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 20 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 x10×10−3\frac{x}{10}\times10^{-3} , where xx is ___________

Step-by-Step Verified Solution

μ=real depth (l1)apparent depth (l2)\mu=\frac{\mathrm{real\,depth}\,(l_1)}{\mathrm{apparent\,depth}\,(l_2)}

=5.255=1.05=\frac{5.25}{5}=1.05

dμμ=dl1l1+dl2l2\frac{d\mu}{\mu}=\frac{dl_1}{l_1}+\frac{dl_2}{l_2}

dμ=(dl1l1+dl2l2)μd\mu = \left( {{{d{l_1}} \over {{l_1}}} + {{d{l_2}} \over {{l_2}}}} \right)\mu

=(0.015.25+0.015.00)×1.05= \left( {{{0.01} \over {5.25}} + {{0.01} \over {5.00}}} \right) \times 1.05

=4110×10−3= {{41} \over {10}} \times {10^{ - 3}}

so x=41x = 41

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