an illuminated object and a screen are placed 60cm apart. What is the focal length and nature of the lens required to produce sharp image on the screen twice the size of the object?

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Solution

Given,
u+v=60 cm
or u=60-v
and magnification, m=2=v/u
or v/(60-v)=2
or v=120-2v
or v=40 cm
Thus, u=60-40=20 cm
Now,
Using lens formula,
1/f=1/v -1/u
or 1/f=1/40-1/(-20)
or Focal length, f=13.3 cm
Since the image is enlarged, so it is a convex lens.(In case of concave lens always a diminished image is formed)
The image formed is real and inverted.

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