The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, then the least count of the microscope is

Options

A. 0.01 cm
B. 0.5 mm
C. 0.01 mm
D. 0.5 cm

Explanation

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

### Step 1: Understand the relationship between the Vernier scale and the main scale
The problem states that 50 divisions on the Vernier scale coincide with 49 divisions on the main scale. This relationship can be expressed mathematically as:
\[ 50 \, \text{VSD} = 49 \, \text{MSD} \]
where VSD is the Vernier Scale Division and MSD is the Main Scale Division.

### Step 2: Calculate the value of one Vernier Scale Division
From the relationship above, we can find the value of one Vernier Scale Division (VSD):
\[ 1 \, \text{VSD} = \frac{49 \, \text{MSD}}{50} \]

### Step 3: Determine the value of one Main Scale Division
The problem states that each Main Scale Division (MSD) is 0.5 mm. Therefore:
\[ 1 \, \text{MSD} = 0.5 \, \text{mm} \]

### Step 4: Substitute the value of MSD into the VSD equation
Now we can substitute the value of one MSD into the equation for VSD:
\[ 1 \, \text{VSD} = \frac{49 \times 0.5 \, \text{mm}}{50} \]
\[ 1 \, \text{VSD} = \frac{24.5 \, \text{mm}}{50} \]
\[ 1 \, \text{VSD} = 0.49 \, \text{mm} \]

### Step 5: Calculate the Least Count
The least count (LC) of the microscope is given by the formula:
\[ \text{Least Count} = 1 \, \text{MSD} - 1 \, \text{VSD} \]
Substituting the values we have:
\[ \text{Least Count} = 0.5 \, \text{mm} - 0.49 \, \text{mm} \]
\[ \text{Least Count} = 0.01 \, \text{mm} \]

### Final Answer
Thus, the least count of the travelling microscope is:
\[ \text{Least Count} = 0.01 \, \text{mm} \]

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