Question

A convex mirror has a focal length of 18 cm. 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? (Answer: 18 cm). Solve the example.

Answer 1

Use the formula
u=f(m-1)/m.
u=18(1/2-1)/(1/2)
u=36(1/2-1)
u=-18cm
So object is 18 cm in left side.

Answer 2

Answer:

Object is at a distance of 18 cm in front of mirror.

Explanation:

As per the question,

Let the distance of object from mirror is = u

      the distance of image from mirror is = v

and the focal length be = f = 18 cm

Formula used:

$Magnification = \frac{-v}{u}$

$\frac{1}{2} = \frac{-v}{u}$

u = -2v

Mirror formula is given by:

$\frac{1}{f}=\frac{1}{u} +\frac{1}{v}$

Put the all the value in this formula, we get

$\frac{1}{18}=\frac{1}{-2v} +\frac{1}{v}$

On solving this, we get

v = 9

and u = -18

That is,

Object is at a distance of 18 cm in front of mirror.

Hence, the distance of the object from the mirror = 18 cm