A person of height 1.8 standing at the centre of a room having equal d...
In this ray diagram h is the height of the man.
Form this ray diagram we can see that the minimum height of the plane mirror is 90 cm, so that the man can see his full image. ( which is equal to half of the height of the man)
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A person of height 1.8 standing at the centre of a room having equal d...
A person of height 1.8 standing at the centre of a room having equal d...
Given, the person's height (h) = 1.8 m and the dimensions of the room (l, b, h) = 10 m
To see the full image of the back wall in the mirror, the person needs to see the top of the back wall from the mirror. This can happen only if the angle of incidence (i) equals the angle of reflection (r) and the reflected ray passes through the top of the back wall.
Let the height of the mirror be 'x' meters above the ground.
Now, the person's eye, the bottom of the mirror, and the top of the back wall form a right-angled triangle.
Using trigonometry, we can say:
tan i = h/l
tan r = h/l
tan (i + r) = (h + x)/l
Adding the first two equations, we get:
tan (i + r) = 2h/l
Substituting this in the third equation, we get:
2h/l = (h + x)/l
x = h
Therefore, the minimum height of the mirror needed is equal to the height of the person, i.e., 1.8 m. Hence, the correct option is C.
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