A man standing in front of a plane mirror finds his image at a distance 6 metre from himself. What is the distance of man from the mirror?

Answer

To solve the problem, we will use the properties of plane mirrors. Here’s a step-by-step solution:

### Step 1: Understand the properties of a plane mirror
A plane mirror creates an image that is the same distance behind the mirror as the object is in front of it. This means if the object (the man) is at a distance \( x \) from the mirror, the image will also be at a distance \( x \) behind the mirror.

### Step 2: Set up the equation
According to the problem, the distance between the man and his image is given as 6 meters. Since the image is formed behind the mirror, the total distance between the man and his image can be expressed as:
\[ \text{Distance from man to mirror} + \text{Distance from mirror to image} = 6 \text{ meters} \]
Since both distances are equal (both are \( x \)), we can write:
\[ x + x = 6 \text{ meters} \]

### Step 3: Simplify the equation
This simplifies to:
\[ 2x = 6 \text{ meters} \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 2:
\[ x = \frac{6}{2} = 3 \text{ meters} \]

### Step 5: Conclusion
Thus, the distance of the man from the mirror is:
\[ \text{Distance from man to mirror} = 3 \text{ meters} \]

### Final Answer
The distance of the man from the mirror is 3 meters.

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