By drawing ray diagrams, explain the formation of image when an object is placed on the principal axis of a convex lens at the following positions:
(i) At infinity
(ii) Beyond 2F₁   
(iii) At 2F₁
(iv) Between F₁ and 2F₁
(v) At focus F₁
(vi) Between focus F₁ and optical centre O.

Image formation by a convex lens: The following are the positions and nature of images formed by a convex lens for different positions of the object:
(i) Object at infinity: The image formed is at focus, real, inverted and highly diminished, as shown in Fig.(a).

Fig.(a). Image formed by a convex lens when object is at infinity

(ii) Object beyond 2F₁: The image formed is between F₂ and 2F₂ on the other side of the lens, real, inverted and diminished, as shown in Fig.(b).

Fig.(b).  Image formed by convex lens when object is beyond 2F₁

(iii) Object at 2F₁: The image formed is at 2F₂, real, inverted and of same size as that of the object, as shown in Fig.(c).

Fig.(c) Image formed by a convex lens when object is at 2F₁

(iv) Object between F₁ and 2F₂: The image formed is beyond 2F₂, real, inverted and magnified, as shown in Fig. (d).

Fig.(d) Image formed by a convex lens when object is between F₁ and 2F₁

(v) Object at F1: The image formed is real, inverted, highly enlarged and at infinity, as shown in Fig.(e).

Fig.(e) Image formed by a convex lens with object at F₁
(vi) Object between F₁ and O: The image is formed on the same side as the object and is virtual, erect and enlarged, as shown in Fig.(f)

Fig.(f) Image formed by a convex lens when object is between F₁ and O