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

The least count (LC) of a travelling microscope is given by: \[ \text{LC} = \frac{\text{Value of one main scale division}}{\text{Number of divisions on the Vernier scale}} = \frac{1 \, \text{msd}}{25} \] Given: 
- 1 msd = \( \frac{15 \, \text{cm}}{300} = 0.05 \, \text{cm} \), 
- Vernier scale has 25 divisions, and each division is equal to 24 divisions of the main scale. 
Thus, the least count is: \[ \text{LC} = \frac{0.05 \, \text{cm}}{25} = 0.002 \, \text{cm} \] 
Thus, the correct answer is (2).