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A convex mirror has a focal length of 18cm. The image of an object kept in front of the mirror is half the height of the object. What is the distance of the object from the mirror?
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Given that,

For convex mirror,

Focal length f= 18cm

And h2= h1/2

Hence, h2/h1 = 1/2

We know that, magnification is given by,

m= h2/h1 = -v/u

Thus, -v/u= 1/2

Hence, v= -u/2

We have mirrors formula as,

1/f = 1/u + 1/v

But, v= -u/2

Then,

1/18= 1/u -2/u

1/18= -1/u

Thus, u= -18 cm

Thus, the object distance is found to be 18 cm.

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