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Question

# The image produced by a concave mirror is one-quarter the size of object. If the object is moved 5 cm closer to the mirror, the image will only be half the size of the object. The focal length of mirror is

A
f=5.0cm
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B
f=2.5cm
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C
f=7.5cm
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D
f=10cm
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Solution

## The correct option is B f=2.5cmIn first case, if object distance is x, image distance =x/4.While it is 2nd case, object distance becomes (x−5 cm) and image distance (x−5 cm)/2. Using mirror formula we get,In first case, =1f=−5xIn second case, 1f=−3(x−5)Solving we get, x=12.5 cm and f=−2.5 cm and hence |f|=2.5 cm.

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