The average size of an Indian face is `24xx16 cm^(2)`. Find the minimum size of a plane mirror required to see the face completely by :
(i) one eyed man
(ii) tow eyed man. (Distance between eyes is `=4 cm`)

Explanation

To find the minimum size of a plane mirror required to see the face completely for both a one-eyed man and a two-eyed man, we can follow these steps:

### Given:
- Average size of an Indian face: 24 cm (height) x 16 cm (width)
- Distance between the eyes: 4 cm

### (i) For a One-Eyed Man:

1. **Determine the Height of the Mirror:**
- The minimum height of the mirror required to see the entire height of the face is half the height of the face.
- Therefore, the minimum height of the mirror \( h_m \) is given by:
\[ h_m = \frac{h}{2} = \frac{24 \, \text{cm}}{2} = 12 \, \text{cm} \]

2. **Determine the Width of the Mirror:**
- For a one-eyed man, he can see only half the width of the face at a time. Therefore, the minimum width of the mirror \( w_m \) is:
\[ w_m = \frac{w}{2} = \frac{16 \, \text{cm}}{2} = 8 \, \text{cm} \]

3. **Final Calculation for One-Eyed Man:**
- The minimum size of the mirror required for a one-eyed man is:
\[ \text{Size of mirror} = h_m \times w_m = 12 \, \text{cm} \times 8 \, \text{cm} \]

### (ii) For a Two-Eyed Man:

1. **Determine the Height of the Mirror:**
- The height of the mirror remains the same as for the one-eyed man since it is based on the height of the face:
\[ h_m = \frac{h}{2} = 12 \, \text{cm} \]

2. **Determine the Width of the Mirror:**
- For a two-eyed man, he needs to see the entire width of the face. The distance between the eyes is 4 cm, so the mirror must be wide enough to reflect the entire width of the face.
- The minimum width of the mirror \( w_m \) is equal to the width of the face:
\[ w_m = 16 \, \text{cm} \]

3. **Final Calculation for Two-Eyed Man:**
- The minimum size of the mirror required for a two-eyed man is:
\[ \text{Size of mirror} = h_m \times w_m = 12 \, \text{cm} \times 16 \, \text{cm} \]

### Summary of Results:
- **For One-Eyed Man:** Minimum size of mirror = \( 12 \, \text{cm} \times 8 \, \text{cm} \)
- **For Two-Eyed Man:** Minimum size of mirror = \( 12 \, \text{cm} \times 16 \, \text{cm} \)