A man of length h requires a mirror of length at least equal to, to see his own complete image

Options

A. (a)`H/4`
B. (b)`H/3`
C. (c)`H/2`
D. (d)H

Answer

To determine the minimum height of a mirror required for a man of height \( h \) to see his complete image, we can follow these steps:

### Step 1: Understanding the Reflection in a Plane Mirror
A plane mirror reflects light in such a way that the angle of incidence is equal to the angle of reflection. This means that the image formed in the mirror is as far behind the mirror as the object is in front of it.

### Step 2: Analyzing the Height Requirement
For a person of height \( h \), the complete image can be seen if the mirror is positioned correctly. The top of the person's head must be visible in the mirror, and the feet must also be visible.

### Step 3: Determining the Minimum Height of the Mirror
To see the entire height of the person, the mirror only needs to be half the height of the person. This is because:
- The line of sight from the eyes to the top of the head will reflect off the mirror.
- The line of sight from the eyes to the feet will also reflect off the mirror.

### Step 4: Conclusion
Thus, the minimum height \( H \) of the mirror required for a person of height \( h \) to see their complete image is given by:
\[ H = \frac{h}{2} \]

### Final Answer
The minimum height of the mirror required is \( \frac{h}{2} \).

---