A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is __________ × 10⁻⁶ m.

Solution

Physics sir · 4 steps

First find what one main scale division is worth, then the least count is that divided by 50.

1. One main division. There are 40 divisions in 1 cm, so 1 MSD = 1/40 cm = 0.025 cm = 0.25 mm.
2. One Vernier division. 50 VSD cover 49 MSD, so 1 VSD = 49/50 MSD. Each Vernier division is a little shorter than a main division.

   LC = 1 MSD - 1 VSD = 1/50 MSD

3. Put in numbers. LC = (0.25 mm)/50 = 0.005 mm = 5 × 10⁻⁶ m.
4. So. The least count of the travelling microscope is 5 × 10⁻⁶ m, so the answer is 5.

The common slip: 20. Taking 1 MSD as 1 mm instead of 0.25 mm gives a least count of 0.02 mm, that is 20, not 5.

The idea to keep. Least count is 1 MSD minus 1 VSD. If n Vernier divisions match n-1 main divisions, LC is 1 MSD divided by n. Always check what 1 MSD really is before dividing.

Answer from the NTA final answer key. Solution by PrepWiser.