If an object is placed at the focus of a convex lens, its image is

Question

Prepp Team · Accepted Answer

Understanding Image Formation by a Convex Lens

When dealing with lenses, understanding where the image forms is crucial. A convex lens is a converging lens, meaning it converges light rays that pass through it. The location and characteristics of the image formed depend on the position of the object relative to the lens.

Object Placed at the Focus of a Convex Lens

The question asks about the image formed when an object is placed specifically at the focus (\(F\)) of a convex lens. This is a special case in lens optics.

Let's trace the paths of a couple of light rays originating from the top of the object placed at \(F\):

A ray starting from the object and travelling parallel to the principal axis hits the convex lens and, after refraction, passes through the principal focus \(F'\) on the other side of the lens.
However, the object itself is placed at the focus \(F\). Let's consider rays from the object at \(F\). A common ray to trace in this scenario is one that passes through the optical centre (\(O\)). A ray passing through the optical centre of a lens goes straight without any deviation.

Now consider a ray starting from the object at \(F\) that is directed towards the lens.

A ray starting from the object at \(F\) and hitting the lens becomes parallel to the principal axis after refraction.

So, we have two key rays after refraction:

A ray that passed through the optical centre (if we trace backwards from the object point). This ray goes straight.
Rays starting from \(F\) and hitting the lens become parallel to the principal axis after refraction.

The rays emerging from the lens after refraction are parallel to each other. Parallel rays do not intersect in the finite plane. They are considered to meet at infinity.

Characteristics of the Image Formed at Infinity

When the refracted rays are parallel, the image is said to be formed at infinity (\(\infty\)). The characteristics of such an image are:

Location: At infinity.
Nature: Real and inverted (these parallel rays would converge at infinity to form a real image).
Size: Highly magnified or infinitely large.

Summarizing Image Formation by Convex Lenses

The position of the object dictates the position and nature of the image. Here's a summary table for convex lenses:

Object Position	Image Position	Nature of Image	Size of Image
At infinity	At \(F\)	Real, Inverted	Highly diminished
Beyond \(2F\)	Between \(F\) and \(2F\)	Real, Inverted	Diminished
At \(2F\)	At \(2F\)	Real, Inverted	Same size
Between \(F\) and \(2F\)	Beyond \(2F\)	Real, Inverted	Magnified
At \(F\)	At infinity	Real, Inverted	Highly magnified
Between the lens (\(O\)) and \(F\)	On the same side as object	Virtual, Erect	Magnified

Based on this, when the object is placed at the focus (\(F\)) of a convex lens, the image is formed at infinity.

Revision Table: Key Concepts for Convex Lenses

Term	Definition
Convex Lens	A converging lens, thicker at the center than at the edges.
Principal Axis	A straight line passing through the optical center and the foci.
Optical Centre (\(O\))	The central point of the lens; rays passing through it are undeviated.
Principal Focus (\(F\), \(F'\))	A point on the principal axis where parallel rays converge (or appear to converge) after passing through the lens. A convex lens has a real focus on the opposite side and a virtual focus on the same side. The 'focus' usually refers to the principal focus where parallel rays converge, which is on the side opposite the object for a convex lens. The point \(F\) where the object is placed in this question is the focus on the same side as the object, such that rays from it become parallel after passing through the lens.
Focal Length (\(f\))	The distance between the optical center and the principal focus.

Additional Information: Applications and Ray Diagrams

The case where an object is placed at the focus of a convex lens and forms an image at infinity is used in devices like searchlights and projectors. In these devices, a light source is placed at the focus of a convex lens (or reflector), producing a parallel beam of light that travels over a long distance.

Drawing ray diagrams is a fundamental skill to understand image formation. Always use at least two principal rays to locate the image. For the case of the object at the focus of a convex lens, the rays emerging are parallel.