An object is placed in front of a lens at a distance which is happened to be its focus of length 20 cm. It forms an image at the same side, where the object is placed but it is smaller than the object and it is in front of the object. Find its image distance.
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It is given that,
Focal length
f=−20cm
hi=3ho
The image is three times the size of the object. So there are two cases.
Case 1. For real image
m=−uv=−3
v=3u
Using mirror’s formula
f1=v1+u1
−201=3u1+u1
u=3−80cm
Case 2. For virtual image
m=u−v=+3
v=−3u
Again using mirror’s formula
−201=−3u1+u1
u=3−40cm
The possible values of u are 3−80cmand3−40cm.
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the answer of the above question is 80 and 40
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