If "50" Vernier divisions are equal to "49" main scale divisions of a traveling microscope and one smallest reading of main scale is "0.5mm" ,the Vernier constant of traveling microscope is

Options

A. 0.01 cm
B. 0.01 mm
C. 0.1 mm
D. 0.1 cm

Answer

To find the Vernier constant of a traveling microscope, we can follow these steps:

### Step 1: Understand the relationship between Vernier and Main Scale divisions
We know from the problem statement that 50 Vernier divisions (VD) are equal to 49 Main Scale divisions (MSD). This can be expressed mathematically as:
\[ 50 \, \text{VD} = 49 \, \text{MSD} \]

### Step 2: Determine the value of one Main Scale division
It is given that the smallest reading of the Main Scale is 0.5 mm. Therefore, we can write:
\[ 1 \, \text{MSD} = 0.5 \, \text{mm} \]

### Step 3: Calculate the length of one Vernier Scale division in mm
From the relationship established in Step 1, we can express one Vernier division in terms of Main Scale divisions:
\[ 1 \, \text{VD} = \frac{49 \, \text{MSD}}{50} \]
Substituting the value of 1 MSD:
\[ 1 \, \text{VD} = \frac{49 \times 0.5 \, \text{mm}}{50} \]
\[ 1 \, \text{VD} = \frac{24.5 \, \text{mm}}{50} \]
\[ 1 \, \text{VD} = 0.49 \, \text{mm} \]

### Step 4: Calculate the Vernier Constant
The Vernier Constant (VC) is defined as the difference between one Main Scale division and one Vernier Scale division:
\[ \text{VC} = \text{MSD} - \text{VD} \]
Substituting the values we have:
\[ \text{VC} = 0.5 \, \text{mm} - 0.49 \, \text{mm} \]
\[ \text{VC} = 0.01 \, \text{mm} \]

### Conclusion
The Vernier constant of the traveling microscope is:
\[ \text{VC} = 0.01 \, \text{mm} \]