Question

a convex mirror has a focal length of 18cm the image of an object kept in front of the mirror is half of the height of the object . what is the distance of the object from mirror

Answer 1

distance of object is 18 or 12

Answer 2

The distance of the object from the mirror is 54 cm.

Explanation:

Given :

A convex mirror has focal length of 18 cm. The image of an object kept in front of the mirror is half of the height of the object.

To find : What is the distance of the object from the mirror?

Solution :

A convex mirror has focal length of 18 cm.

Let the object placed at O=x cm.

The image of an object kept in front of the mirror is half of the height of the object.

So, Image is at $I=\frac{x}{2}cm$

The formula to find the relationship is

$\frac{I}{O}= \frac{v}{u}$

$\frac{\frac{x}{2}}{x}= \frac{v}{u}$

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

Again the focal length formula is

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

Substitute the values,

$\frac{1}{18}= \frac{1}{u}+\frac{1}{\frac{u}{2}}$

$\frac{1}{18}= \frac{1}{u}+\frac{2}{u}$

$\frac{1}{18}= \frac{3}{u}$

Cross multiply,

$u=3\times 18$

$u=54$

Therefore, The distance of the object from the mirror is 54 cm.✅

_______________________________