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Question

A concave mirror produces a real image twice the size of the object when placed at a distance of 22.5 cm from it. Where should be object be placed so that the size of the image becomes three times that of the object?

A
20 cm
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B
22.5 cm
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C
30.4 cm
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D
24 cm
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Solution

The correct option is A 20 cm
Case 1 :
Magnification m=2 (image is real)
Object distance u=22.5cm
From m=vu
2=vu
We get v=2u=45cm
Using 1f=1v+1u
1f=145122.5=1245
1f=345
f=15cm

Case 2 :
Let the new object distance be x i.e. u=x now.
Magnification m=3 (image is real)
From m=vu
3=vx v=3x
Using 1f=1v+1u
115=13x+1x

115=1+33x
3x=60
x=+20cm.
Hence, object must be placed at 20 cm.

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