A person has `D` cm wide face and his two eyes are separated by d cm. The minimum width of a mirror required for the person to view his complete face is

Options

A. `(D+d)/(2)`
B. `(D-d)/(4)`
C. `(D+d)/(4)`
D. `(D-d)/(2)`

Explanation

To determine the minimum width of a mirror required for a person to view his complete face, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Let the width of the person's face be \( D \) cm.
- The distance between the two eyes is \( d \) cm.
- We need to find the minimum width of a mirror that allows the person to see their entire face.

2. **Visualizing the Setup**:
- Imagine the person standing in front of a plane mirror. The mirror reflects the image of the person’s face.
- The eyes of the person are at a distance \( d \) apart, and the face extends \( D \) cm wide.

3. **Ray Diagram**:
- Draw a ray diagram where the rays from the edges of the face reach the mirror and reflect back to the eyes.
- The rays from the outer edges of the face will hit the mirror and reflect back to the eyes.

4. **Calculating the Required Width**:
- For the person to see their entire face, the mirror must be wide enough to reflect the rays from both edges of the face to the eyes.
- The minimum width of the mirror can be calculated as follows:
- The distance from the center of the face to one edge is \( \frac{D}{2} \).
- The distance from the center of the eyes to the edge of the eyes is \( \frac{d}{2} \).
- Therefore, the total width of the mirror required is:
\[ \text{Width of mirror} = \frac{D}{2} + \frac{d}{2} = \frac{D + d}{2} \]

5. **Final Expression**:
- The minimum width of the mirror that allows the person to view their complete face is:
\[ \text{Minimum Width} = D - \frac{d}{2} \]

### Conclusion:
Thus, the minimum width of the mirror required for the person to view his complete face is \( D - \frac{d}{2} \).