For the determination of refractive index of glass slab, a...

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm) :

Options

A $0.001$
B $0.002$
C $0.0005$
D $0.0025$

Correct answer

B. $0.002$

Step-by-step solution

\begin{aligned} & 300 \mathrm{msd}=15 \mathrm{~cm} \\ & 1 \mathrm{msd}=\frac{15}{300} \mathrm{~cm}=0.05 \mathrm{~cm} \\ & 25 \mathrm{vsd}=24 \mathrm{msd} \\ & 1 \mathrm{vsd}=\frac{24}{25} \mathrm{msd} \\ & \mathrm{LC}=1 \mathrm{msd}-1 \mathrm{vsd}\end{aligned}

\begin{aligned}<br/>& \mathrm{LC}=1 \mathrm{msd}-\frac{24}{25} \mathrm{msd}=\frac{1}{25} \mathrm{msd} \\ & \mathrm{LC}=\frac{1}{25} \times 0.05=0.002 \mathrm{~cm}<br/>\end{aligned}

correct option (2)

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