Question

A microscope has its main scale with 20 divisions in 1 cm and vernier scale with 25 divisions, the length of which is equal to the length of 24 divisions of main scale. The least count of microscope is

• A. 0.002 cm
• B. 0.001 cm
• C. 0.02 cm
• D. 0.01 cm

Answer 1

The correct option is A 0.002 cm

Least count of the microscope = Least count of the main scale- least count of the vernier scale
Now,
Least count of the main scale = $\frac{1}{20}=0.050$ cm.
Least count of the vernier scale:
In the vernier scale, 24 divisions of the main scale = 25 divisions of the vernier scale
Thus, length of vernier scale = $\frac{24}{25}=0.96$ cm.
Hence, least count of vernier scale = $\frac{0.96}{20}=0.048$
Hence, least count of microscope = $0.05-0.048=0.002$ cm.