Two plane mirrors are kept such that angle between their reflecting surfaces is `40^(@)`. A point object is kept symmetrically with respect to the mirrors. The total number of images formed by one mirror is :

Options

A. 8
B. 9
C. 4
D. 5

Answer

To solve the problem of finding the total number of images formed by one of the two plane mirrors when they are positioned at an angle of 40 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
We have two plane mirrors (let's call them Mirror 1 and Mirror 2) placed at an angle of 40 degrees to each other. A point object is placed symmetrically with respect to the mirrors.

2. **Using the Formula for Number of Images**:
The formula to calculate the total number of images formed by two mirrors at an angle θ is given by:
\[ n = \frac{360}{\theta} - 1 \]
where \( n \) is the total number of images formed.

3. **Substituting the Angle**:
Here, the angle \( \theta \) is 40 degrees. We substitute this value into the formula:
\[ n = \frac{360}{40} - 1 \]

4. **Calculating the Total Number of Images**:
Now, we perform the calculation:
\[ n = 9 - 1 = 8 \]
So, the total number of images formed by both mirrors is 8.

5. **Finding the Number of Images Formed by One Mirror**:
Since the question asks for the number of images formed by one mirror, we divide the total number of images by 2 (because the images are symmetrically formed by both mirrors):
\[ \text{Images by one mirror} = \frac{8}{2} = 4 \]

6. **Final Answer**:
Therefore, the total number of images formed by one mirror is **4**.