Question

To form an image twice the size of the object, using a convex lens of focal length $20cm$, the object distance must be

• A. < 20 cm
• B. > 20 cm
• C. < 20 cm and between 20 cm and 40 cm
• D. equal to 20 cm

Answer 1

The correct option is C

< 20 cm and between 20 cm and 40 cm

Let object distance be u
image distance be v
and focal length be f
Given that the image is twice the size of the object which means we want a magnified image.
As per the different cases of ray diagrams, we know that
A convex lens forms real and inverted image till the object is brought from infinity to focus. So $u>f$ for a real image. The convex lens produces magnified real image when the object is placed between $f$ and $2f$.

Also, a convex lens forms virtual, magnified and erect image when the object is placed between the pole and the focus. So $u<f$ for a virtual image.

So for a virtual magnified image, object distance should be less than $20cm$ and for real magnified image, object distance must be between $20cm$ and $40cm$.