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Question

# A plane mirror is placed 22.5cm in front of a concave mirror of focal length 10cm. An object can be placed between the two mirrors so that the first image in both the mirror coincides. The object distance from the spherical mirror is

A
15cm
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B
25cm
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C
30cm
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D
20cm
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Solution

## The correct option is C 15cmIt can seen from the figure that, if the object is placed at a distance x from the concave mirror, its distance from the plane mirror will be (22.5−x). So plane mirror equal and erect image of object at a distance (22.5−x) behind the mirror. Now according to the given problem, the image coincided with the image formed by the plane mirror, therefore for concave mirror.v=−[22.5+22.5−x]=−(45−x) and object distanceu=−xgiven focal length isf=−10So using mirror formula,1v+1u=1f1−(45−x)+1−x=1−10⟹4545x−x2=110x2−45x+450=0(x−30)(x−15)=0Hence x=30cm or x=15cm.But as the distance between the two mirror is 22.5, x=30 is not admissible . So the object must be at a distance of 15 cm from the concave mirror

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