A man stands in front of a large vertical plane mirror.His height is 1.8 m. The distance of image from the man is 4 m. At what distance is the man standing from the mirror?

Answer

To solve the problem step by step, we can follow this reasoning:

### Step 1: Understand the relationship between the object and the image in a plane mirror.
In a plane mirror, the distance of the image from the mirror is equal to the distance of the object (the man) from the mirror. If the man is standing at a distance \( x \) from the mirror, then the image will also be at a distance \( x \) behind the mirror.

### Step 2: Set up the equation based on the given information.
We know that the distance between the man and his image is given as 4 meters. Since the image is behind the mirror, the total distance between the man and the image can be expressed as:
\[ \text{Distance between man and image} = \text{Distance from man to mirror} + \text{Distance from mirror to image} \]
This can be written as:
\[ 4 \text{ m} = x + x \]
where \( x \) is the distance from the man to the mirror.

### Step 3: Simplify the equation.
From the equation above, we can simplify it:
\[ 4 \text{ m} = 2x \]

### Step 4: Solve for \( x \).
To find \( x \), we divide both sides of the equation by 2:
\[ x = \frac{4 \text{ m}}{2} = 2 \text{ m} \]

### Step 5: State the final answer.
Thus, the distance at which the man is standing from the mirror is:
\[ \text{Distance from the man to the mirror} = 2 \text{ m} \]

### Summary of the Solution:
The man is standing 2 meters away from the mirror.

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