Question

A convex lens forms a real and inverted image of a needle at a distance of $50cm$ from it. Where is the needle placed in front of the convex lens if the size of the image is equal to the size of the object? Also find the power of the lens.

• A. Object distance $=50cm$
  Power $=2D$
• B. Object distance$=25cm$
  Power $=4D$
• C. Object distance$=50cm$
  Power $=4D$
• D. Object distance$=25cm$
  Power $=2D$

Answer 1

The correct option is C Object distance$=50cm$

Power $=4D$
For a lens, when image size equals the object size, the object is placed at center of curvature. In this case, image distance is equal to the object distance.
Hence, object distance is $50cm$.

Now, focal length of a lens is half of the radius of curvature.
$f=\frac{50}{2}=25cm$
From definition of Power,
$P=\frac{1}{f}$
$P=\frac{1}{0.25}=4D$