The height of a room is 6m.A person of height 1.5m is standing at the centre of a room.A plane mirror is to be fixed on front wall the minimum vertical lenght of the mirror so that the person can see complete image of his own and the wall behind him?
draw a ray diagram. To see his feet, the base of the mirror must be 1/2 way between the floor and his eyes.
if he can see his feet, he can see the base of the wall behind.
Now to see the top of the wall behind, the top of the mirror must be 1/2 way up from his eyes to the top of the ceiling.
So figure the distance between the base and the top of the mirror.
To determine the minimum vertical length of the mirror required, we need to consider the geometry of the situation.
Let's analyze the scenario step by step:
1. The person's height is 1.5m, and they are standing at the center of the room. Since the room's height is 6m, there are 4.5m (6m - 1.5m) of empty space above the person.
2. When a person looks into a plane mirror, they see their own image as if it is coming from behind the mirror. So, the person in front of the mirror will see a virtual image.
3. In order for the person to see the complete image of themselves and the wall behind them, the mirror should cover the entire vertical distance between the person's eye level and the wall behind them.
4. The person's eye level is at a height of 1.5m, and the distance from the person's eye level to the wall behind them is 4.5m (the empty space above them).
5. Therefore, the minimum vertical length of the mirror required can be calculated by summing the person's eye level and the empty space above them: 1.5m + 4.5m = 6m.
Hence, the minimum vertical length of the mirror required for the person to see their complete image and the wall behind them is 6m.