David is observing his image in a plane mirror. The distance between the mirror and his image is 4 m. If he moves 1 m towards the mirror, then the distance between David and his image will be
$(i).\ 3\ m$
$(ii).\ 5\ m$
$(iii).\ 6\ m$
$(iv).\ 8\ m$
The correct answer is $(iii)\ 6\ m$.
Explanation:
Given:
David is observing his image in a plane mirror. The distance between the mirror and his image is 4 m.
To do:
To find the distance between David and his image if he moves $1\ m$ towards the mirror.
Solution:
To calculate the distance between David and his image let us know how and where the image is formed by a plane mirror.
Image formation by a plane mirror:
The image formed by a plane mirror is virtual $(behind\ the\ mirror)$, erect $(upright)$, laterally inverted, same as that of the size of the object, and is equal to the distance of the object from the mirror as shown in the ray diagram below.
![](/assets/questions/media/148618-60907-1664134945.png)
Distance between David and his image:
The given distance between David's image and the mirror is $4\ m$.
This means that the distance between David and the mirror is also $4\ m$.
When David moves $1\ m$ towards the mirror, then the distance between David and mirror $=4\ m-1\ m=3\ m$
The image will be formed at the same distance$(3\ m)$ behind the mirror.
Therefore, the distance between David and his image $=3\ m+3\ m=6\ m$.
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