Question

he distance between the object and its image formed by a plane mirror appears to be 18 cm. What is the distance between mirror and the object?

Answer 1

The distance between mirror and the object is 9cm.

Explanation:

Plane mirror is a flat reflective surface.

Image formed by a plane mirror has following properties:

• Image is always virtual i.e. behind the mirror.
• Laterally inverted images are formed.
• Erect images are formed.
• Size of image behind the mirror is equal to the size of object in-front of the mirror.
• Distance of the image from the mirror is the same as the distance between object and the mirror.

So, when distance between object and image is 18 cm, then the distance between the object and the mirror is half of that distance i.e. 9cm.

Answer 2

Given:

Distance between object and image = 18 cm

To find:

the distance between the mirror and the object

Solution:

The image generated by a plane mirror forms at the same distance behind the mirror as it is between the object snd the mirror.  

Therefore, object distance from the mirror equals image distance from the mirror.

Let the distance between the object and the mirror be $x$.

Then the distance between the mirror and the reflection is also $x$.

Now, according to the problem,

$x+x=18$

⇒$2x=18$

⇒$x=9$

Hence, the distance between mirror and the object is 9 cm.