If a man requires a mirror of 0.9m as to see the whole of himself in the mirror when he is standing 2m away from the mirror. How much mirror does he require when he now stands 6m from the mirror?
The same mirror length is required: 0.9 m , which is half his height. The mirror is always half way between the man and his image.
To calculate how much mirror the man requires when he stands 6m from the mirror, we need to understand the relationship between the distance of the man from the mirror and the size of the mirror.
In this case, the man requires a mirror of 0.9m to see his whole self when he is standing 2m away from the mirror. This means that the height of the mirror is related to the distance to the mirror.
We can assume that the height of the man remains constant (since it is not mentioned in the question), and only the distance changes. From this, we can establish a proportion:
Distance to mirror / Height of mirror = Constant
Let's call the distance to the mirror "d" and the height of the mirror "h". Using the values mentioned in the question, we can write the proportion as:
2m / 0.9m = 6m / h
Now, we can solve for "h", the height of the mirror when the man stands 6m from the mirror:
2m / 0.9m = 6m / h
Cross-multiplying, we get:
2m * h = 6m * 0.9m
2h = 5.4
Dividing by 2, we find:
h = 5.4 / 2
h = 2.7
Therefore, the man requires a mirror with a height of 2.7m when he stands 6m away.