A man of height `170cm`wants to see his complete image in a plane mirror(while standing).His eyes are at a height of `160cm`from the ground.

Options

A. Minimum length of the mirror = 80 cm
B. Minimum length of the mirror = 85 cm
C. Bottom of the mirror should be at a height 80 cm
D. Bottom of the mirror should be at a height of 85 cm

Explanation

To solve the problem of determining the minimum height of a plane mirror required for a man of height 170 cm to see his complete image while standing, we can follow these steps:

### Step 1: Understand the Problem
The man is 170 cm tall, and his eyes are at a height of 160 cm from the ground. We need to find out the minimum height of the mirror that allows him to see his entire reflection.

### Step 2: Analyze the Reflection in the Mirror
In a plane mirror, the height of the mirror required to see the full image is half the height of the person. This is because the light reflecting from the top of the head and the bottom of the feet will meet at the eyes, and thus the mirror only needs to be half the height of the person.

### Step 3: Calculate the Required Height of the Mirror
Since the man is 170 cm tall, the minimum height of the mirror can be calculated as follows:
\[ \text{Minimum height of the mirror} = \frac{\text{Height of the man}}{2} = \frac{170 \text{ cm}}{2} = 85 \text{ cm} \]

### Step 4: Determine the Position of the Mirror
The bottom of the mirror should be positioned such that the man can see his feet. Since his eyes are at 160 cm, and the mirror needs to reflect down to the feet, we can calculate the height at which the bottom of the mirror should be placed.

The distance from the eyes to the feet is:
\[ \text{Height of the man} - \text{Height of the eyes} = 170 \text{ cm} - 160 \text{ cm} = 10 \text{ cm} \]
Since the mirror needs to reflect the full height, the bottom of the mirror should be at:
\[ \text{Height of the eyes} - \left(\frac{\text{Height of the mirror}}{2}\right) = 160 \text{ cm} - \left(\frac{85 \text{ cm}}{2}\right) = 160 \text{ cm} - 42.5 \text{ cm} = 117.5 \text{ cm} \]

### Step 5: Conclusion
Thus, the minimum height of the mirror required is 85 cm, and the bottom of the mirror should be at a height of 117.5 cm from the ground.

### Final Answer
- Minimum height of the mirror: **85 cm**
- Height of the bottom of the mirror from the ground: **117.5 cm**

---