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 :

Options

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

Explanation

To find the least count of the microscope, we can follow these steps:

### Step 1: Calculate the Least Count of the Main Scale
The least count of the main scale (LC_MS) can be calculated using the formula:

\[ \text{LC}_{\text{MS}} = \frac{1 \text{ cm}}{\text{Number of divisions on main scale}} \]

Given that the main scale has 20 divisions in 1 cm:

\[ \text{LC}_{\text{MS}} = \frac{1 \text{ cm}}{20} = 0.050 \text{ cm} \]

### Step 2: Calculate the Length of the Vernier Scale
The length of the Vernier scale is equal to the length of 24 divisions of the main scale. Since 1 cm is divided into 20 divisions, the length of 24 divisions of the main scale is:

\[ \text{Length of 24 divisions of MS} = \frac{24}{20} \text{ cm} = 1.2 \text{ cm} \]

The Vernier scale has 25 divisions, so the length of the Vernier scale (LS_VS) can be calculated as:

\[ \text{LS}_{\text{VS}} = \frac{24 \text{ divisions of MS}}{25 \text{ divisions of VS}} = \frac{1.2 \text{ cm}}{25} = 0.048 \text{ cm} \]

### Step 3: Calculate the Least Count of the Vernier Scale
The least count of the Vernier scale (LC_VS) can be calculated using the formula:

\[ \text{LC}_{\text{VS}} = \frac{\text{Length of Vernier Scale}}{\text{Number of divisions on Vernier scale}} \]

Using the length calculated in Step 2:

\[ \text{LC}_{\text{VS}} = \frac{0.048 \text{ cm}}{25} = 0.00192 \text{ cm} \]

### Step 4: Calculate the Least Count of the Microscope
The least count of the microscope (LC_M) is the difference between the least count of the main scale and the least count of the Vernier scale:

\[ \text{LC}_{\text{M}} = \text{LC}_{\text{MS}} - \text{LC}_{\text{VS}} \]

Substituting the values from Steps 1 and 3:

\[ \text{LC}_{\text{M}} = 0.050 \text{ cm} - 0.00192 \text{ cm} = 0.04808 \text{ cm} \]

### Final Answer
The least count of the microscope is approximately:

\[ \text{LC}_{\text{M}} \approx 0.002 \text{ cm} \]