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. (a)4
B. (b)1
C. (c)2
D. (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 1: Understand the setup
We have two plane mirrors positioned at a right angle (90 degrees) to each other. The man is standing between these mirrors, using his right hand to comb his hair.

### Step 2: Use the formula for the number of images
The formula to calculate the number of images formed by two mirrors at an angle \( \theta \) is given by:

\[ \text{Number of images} = \frac{360}{\theta} - 1 \]

In our case, since the mirrors are at a right angle, \( \theta = 90^\circ \).

### Step 3: Calculate the number of images
Substituting \( \theta = 90^\circ \) into the formula:

\[ \text{Number of images} = \frac{360}{90} - 1 = 4 - 1 = 3 \]

So, a total of 3 images will be formed.

### Step 4: Determine how many images show the right hand
Now, we need to analyze how many of these images will show the man using his right hand.

1. The first image will appear as if the man is using his left hand.
2. The second image will also appear as if he is using his left hand.
3. The third image will appear as if he is using his right hand.

Thus, out of the 3 images formed, only 1 image will show the man using his right hand.

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

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