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.
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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