A small object is placed on the focus on the left side of a convex lens. Where will be the image formed?

Correct — A. Place the object at the focus (F) and every ray leaving it emerges from a convex lens parallel to the principal axis.

Parallel rays never meet at any finite distance, so the image is thrown to infinity — and on the far side of the lens from the object, which is the right side here.

The lens formula agrees: with u = −f, 1/v = 0, so v is infinite. Option (a).

Why the others are wrong

• (b)
  At infinity on the left side of the lens. — Infinity on the left puts the image on the object's own side. Light travels left to right through the lens, so a real image can only form beyond it.
• (c)
  At the focus on the right side of the lens. — The focus on the right is the answer to the reverse case — an object at infinity, whose parallel rays converge at F after refraction.
• (d)
  At the centre on the right side of the lens. — The centre gives no image at all: the optical centre lies inside the lens. Read as the centre of curvature (2F), it is where an object at 2F would image, not one at F.

A convex lens converges light, and two ray rules settle every case. A ray through the optical centre goes straight on, and a ray parallel to the axis bends through the far focus.

Run those backwards for an object sitting at F: the emergent rays come out parallel to each other, and parallel rays meet only at infinity.

The position ladder is worth memorising. Object beyond 2F images between F and 2F. At 2F it images at 2F. Between F and 2F it images beyond 2F. At F it images at infinity.

Key facts

• An object at the focus of a convex lens gives an image at infinity that is real, inverted and highly enlarged.
• Rays diverging from the focus emerge parallel to the principal axis after refraction through a convex lens.
• Substituting u = −f in the lens formula gives 1/v = 0, so v is infinite.

Common traps

• Swapping the two infinity cases — object at F gives image at infinity, object at infinity gives image at F.
• Placing a real image on the same side of the lens as the object.

No directly related past PYQ was found.