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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Physics
Chapter
Ray Optics

JEE Main 2024 · 6 April · Evening Shift · Physics · Ray Optics

In finding out refractive index of glass slab the following...

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division =49MSD;20=49 \mathrm{MSD} ; 20 divisions on main scale in each cm\mathrm{cm} For mark on paper MSR=8.45 cm,VC=26\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26 For mark on paper seen through slab MSR =7.12 cm,VC=41=7.12 \mathrm{~cm}, V C=41 For powder particle on the top surface of the glass slab MSR=4.05 cm,VC=1\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1 (MSR = Main Scale Reading, VC = Vernier Coincidence) Refractive index of the glass slab is :

Options

  1. A1.52
  2. B1.35
  3. C1.42
  4. D1.24

Correct answer

C. 1.42

Step-by-step solution

1MSD=1 cm20=0.05 cm1VSD=4950MSD=4950×0.05 cm=0.049 cmLC=1MSD−1VSD=0.001 cm\begin{aligned} & 1 \mathrm{MSD}=\frac{1 \mathrm{~cm}}{20}=0.05 \mathrm{~cm} \\ & 1 \mathrm{VSD}=\frac{49}{50} \mathrm{MSD}=\frac{49}{50} \times 0.05 \mathrm{~cm}=0.049 \mathrm{~cm} \\ & \mathrm{LC}=1 \mathrm{MSD}-1 \mathrm{VSD}=0.001 \mathrm{~cm} \end{aligned}
For mark on paper, L1=8.45 cm+26×0.001 cm=84.76 mm\mathrm{L}_1=8.45 \mathrm{~cm}+26 \times 0.001 \mathrm{~cm}=84.76 \mathrm{~mm} For mark on paper through slab, L2=7.12 cm+41×0.001 cm=71.61 mm\mathrm{L} 2=7.12 \mathrm{~cm}+41 \times 0.001 \mathrm{~cm}=71.61 \mathrm{~mm} For powder particle on top surface, ZE=4.05 cm+1×0.001 cm=40.51 mm\mathrm{ZE}=4.05 \mathrm{~cm}+1 \times 0.001 \mathrm{~cm}=40.51 \mathrm{~mm}
∴ actual L1=84.76−40.51=44.25 mm actual L2=71.61−40.51=31.10 mm L2=L1μ⇒μ=L1 L2=44.2531.10=1.42\begin{aligned} \therefore & \text{ actual } \mathrm{L}_1=84.76-40.51=44.25 \mathrm{~mm} \\ & \text{ actual } \mathrm{L}_2=71.61-40.51=31.10 \mathrm{~mm} \\ & \mathrm{~L}_2=\frac{\mathrm{L}_1}{\mu} \\ \Rightarrow & \mu=\frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{44.25}{31.10}=1.42\end{aligned}
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