Question

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):

• A. 0.001
• B. 0.002
• C. 0.0005
• D. 0.0025

Hint:

The least count of a vernier scale is the difference between the value of one main scale division and the value of one vernier scale division.

Answer 1

The Correct Option is B

To determine the least count of the travelling microscope, we must first define least count and its application to this instrument. The least count (LC) represents the smallest measurable value accurately. For a travelling microscope, this is calculated by:

\(LC = \frac{\text{Value of 1 main scale division}}{\text{Number of vernier scale divisions}}\)

Given Data:

• Main scale: 300 divisions span 15 cm.
• Vernier scale: 25 divisions match 24 main scale divisions.

Calculations:

1. Value of 1 main scale division:

\(\text{Value of 1 main scale division} = \frac{15 \text{ cm}}{300} = 0.05 \text{ cm}\)

1. Least count calculation:

Since 25 vernier divisions equal 24 main scale divisions, one vernier division is:

\(\frac{24 \text{ main scale divisions}}{25}\\)

1. Substitution into the least count formula:

\(LC = \frac{0.05 \text{ cm}}{25} = 0.002 \text{ cm}\)

The least count of the travelling microscope is therefore 0.002 cm.

Conclusion:

The correct value is 0.002.