Two plane mirrors are at right angles to each other. A man stands between them and combs his hair with his right hand. In how many of the images will he be seen using his right hand

Options

A. None
B. 1
C. 2
D. 3

Answer

To solve the problem of how many images of a man combing his hair with his right hand will be seen in two plane mirrors placed at right angles to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two plane mirrors that are positioned at a right angle (90 degrees) to each other.
- A man is standing between these mirrors, combing his hair with his right hand.

2. **Using the Formula for Total Images**:
- The formula to calculate the total number of images (N) formed by two mirrors at an angle θ is given by:
\[ N = \frac{360}{\theta} - 1 \]
- Here, θ = 90 degrees (since the mirrors are at right angles).

3. **Calculating Total Images**:
- Substituting θ into the formula:
\[ N = \frac{360}{90} - 1 = 4 - 1 = 3 \]
- Therefore, a total of 3 images will be formed.

4. **Identifying the Hand Used**:
- The man is using his right hand to comb his hair.
- In the images formed, we need to determine how many of these images will show him using his right hand.

5. **Determining the Images with Right Hand**:
- Out of the 3 images formed, we need to find out how many show the right hand.
- Since the man is standing between the mirrors, the images will reflect his actions.
- Typically, one of the images will show the right hand as it is, while the other images will show the left hand due to the nature of reflection.

6. **Final Count of Right Hand Images**:
- Since there are 3 images in total and 2 of them will show the left hand, only 1 image will show the right hand.
- Therefore, the final answer is that he will be seen using his right hand in **1 image**.

### Final Answer:
The man will be seen using his right hand in **1 image**.

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