The images of two persons A and B standing $1 m$ apart in front of a plane mirror are A' & B' respectively. Image A' is at a distance of $2 m$ from the mirror. Select the statements which are true.

Distance between A & B' is equal to distance between A' & B

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Distance between A & B is less than distance between A' & B

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Distance between B & B' is equal to distance between A & A'

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Distance between B & mirror is equal to distance between A & B

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Solution

The correct option is D Distance between B & mirror is equal to distance between A & B
A plane mirror forms the image of an object such that both the object and the image are equidistant from the mirror. Here, A' is the image of A and B' is the image of B.

Distance between A' & mirror is $2 m$ , so distance A & mirror is also $2 m$ .

Distance between A & B is $1 m$ , so distance between A' & B' is also $1 m$ .

Distance between A (or A') & mirror is $2 m$ , A & B is 1, so distance between B (or B') & mirror is $1 m$ .

Distance between B & mirror $= 1 m$
Distance between A & B' $= 2 + 1 = 3 m$
Distance between A' & B $= 1 + 2 = 3 m$
Distance between A & B $= 1 m$
Distance between B & B' $= 1 + 1 = 2 m$
Distance between A & A' $= 2 + 2 = 4 m$

Accordingly, correct options can now be easily chosen.

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