Question

Draw the ray diagrams to show the formation of images when:

[(a)] Object is placed in front of a converging lens between its focus (F) and optical centre (O)
[(b)] Object is placed between focus (F) and twice the distance of focus (2F)
State the nature of the images.

Hint:

For convex lenses:

Object between \( O \) and \( F \) → Virtual, erect, magnified image.
Object between \( F \) and \( 2F \) → Real, inverted, magnified image beyond \( 2F \).

Answer 1

(a) Object between optical centre (O) and focus (F): Ray diagram instructions for (a)

Draw a convex lens with principal axis.
Mark the optical centre \( O \), focus \( F \), and twice the focal length \( 2F \) on both sides.
Place the object between \( O \) and \( F \).
Draw:

A ray parallel to the principal axis → refracted through the far focus.
A ray passing through the optical centre \( O \) → goes undeviated.

The two refracted rays diverge, so extend them backward to meet behind the object.

Nature of image:

Virtual
Erect
Magnified
Formed on the same side as the object

(b) Object between \( F \) and \( 2F \): Ray diagram instructions for (b)

Place the object between \( F \) and \( 2F \) in front of a convex lens.
Draw:

A ray parallel to the principal axis → refracted through far focus.
A ray through the optical centre \( O \) → goes undeviated.

The rays meet on the other side of the lens to form the image.

Nature of image:

Real
Inverted
Magnified
Formed beyond \( 2F \) on the opposite side