Convex lens, terminology, Image formation, Lens formula, Practice problems, FAQs

Have you burned paper with the help of magnifying lens in your childhood? Have you thought about how it is possible? When a light ray from the Sun comes on a converging lens it is nearly parallel. Hence the energy associated with it is also distributed over the area. After the refraction from the converging lens the rays are concentrated on a point, along with that energy also gets concentrated on a single point. Now if this point falls on a paper, it will start burning. Let's understand the convex lens in detail!

Table of content

Introduction
Important Terminologies Used for Convex Lenses
Image Formation in Convex Lens
Lens formula for convex lens
Practice problems
FAQs

Introduction

Hey there, future scientists! If you’ve ever used a magnifying glass to look at a tiny ant or wondered how your camera captures sharp photos, you’ve already encountered the magic of a convex lens. Whether you are preparing for school exams or competitive tests like JEE/NEET, understanding how this lens works is essential.

In this guide, we’ll break down everything you need to know in simple, conversational English—just like we’re chatting in a classroom!

What Exactly Is a Convex Lens?

Think of a convex lens as a "chubby" piece of transparent glass. It is thicker in the middle and gradually becomes thinner toward the edges.

Because of this shape, it has a special superpower: it bends incoming light rays so that they meet at a single point. This is why a convex lens is also called a converging lens.

Imagine a group of friends running from different corners to meet at one favorite hangout spot—that’s exactly what light rays do when they pass through a convex lens!

Different Types of Convex Lenses

In physics labs and optical instruments, convex lenses appear in different forms. The most common types include:

Double-Convex Lens: Both surfaces bulge outward. This is the most commonly used convex lens.
Plano-Convex Lens: One surface is flat, while the other bulges outward.
Concavo-Convex Lens: One surface curves inward and the other outward, but the center remains thicker than the edges.

How Does Image Formation by a Convex Lens Work?

To understand how images are formed, we use three simple Golden Rules of ray optics:

The Straight Path Rule: A light ray passing through the optical centre of the lens travels straight without bending.
The Parallel Ray Rule: A ray parallel to the principal axis bends and passes through the focus (F) after refraction.
The Focus Ray Rule: A ray passing through the focus emerges parallel to the principal axis.

Summary Table: Image Formed by a Convex Lens

The nature and size of the image depend on the position of the object. The table below works as a quick reference:

Position of Object	Position of Image	Nature of Image	Size of Image
At Infinity	At Focus (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	Enlarged
At Focus (F)	At Infinity	Real & Inverted	Highly Enlarged
Between F and Optical Centre	Same Side as Object	Virtual & Erect	Enlarged

Note: In the last case, the image is virtual because the light rays do not actually meet; they only appear to come from a point behind the lens.

The Core Formulas You Need to Know

To solve numerical problems efficiently, remember these two important formulas. Here, u is object distance, v is image distance, and f is focal length.

1. Lens Formula

1/f = 1/v + 1/u

2. Magnification (m)

Based on height: m = h_i / h_o
Based on distance: m = v / u

Pro-Tip: If magnification is negative, the image is real and inverted. If positive, the image is virtual and erect.

Why Does This Matter? (Real-World Applications)

Convex lenses play a crucial role in everyday life:

Magnifying Glass: Produces a large, virtual image when the object is placed close to the lens.
Eyeglasses: Used to correct farsightedness by focusing light correctly on the retina.
Cameras & Projectors: Form real, sharp images on sensors or screens.
Microscopes: Use multiple convex lenses to magnify tiny objects invisible to the naked eye.

The radius of both the spheres can be the same or can be different. A convex lens is thin at the edges and is thick in the middle. Also, these lenses have a property that they can converge all the rays falling on it. Therefore, these types of lenses are also known as converging lenses.

The types of converging lenses are shown in the figure below.

Now let's see the terms related to convex lenses.

Important Terminologies Used for Convex Lenses

1. Center of curvature (C): Convex lenses are a combination of two spherical surfaces as shown in the figure. These spherical surfaces are parts of two different spheres. Center of these shapes is known as the center of curvature. The center of curvature of the first surface is C₁, and the center of curvature of the second surface is C₂.

For the lenses, having one surface as plane, and the other surface as spherical. The center of the plane surface is at infinity. For the spherical part, the center is at C as shown in the figure

2. Radius of curvature: The distance between the center of the lens and the center of curvature is known as the radius of curvature.

3. Principal axis: The line joining the center of curvatures of two bounding surfaces is known as the principal axis.

4. Optical center: An optical center is a point for a given lens through which any ray passes without any deviation. For a biconcave or a biconvex lens, the optical center of the lens is located at the geometrical center of the lens.

Note:

The optical center can lie inside, on the surface, or outside the lens, depending upon the values of R₁ and R₂.

5. Focus: Lens have two focuses because the light can strike the lens from both the sides. They are known as first principal focus and second principal focus.

First principal focus:

For a convex lens, it is the point on the principal axis where the object is kept; the rays from that object become parallel to the principal axis after passing through the lens (i.e., the image forms at infinity).

Second principal focus

For a convex lens, it is the point on the principal axis where the rays parallel to the principal axis converge after passing through the lens.

Note: The second principal focus is the main focus. In a question, if they mention focus, we have to take that as the second principal focus.

6. Focal plane: The rays parallel to each other and not parallel to the principal axis converge at a point after passing through the lens that lies on the plane containing the focus of the lens. This plane is known as the focal plane.

Image Formation in Convex Lens

Position of the image from a convex lens depends upon the position of the object. Here are some cases that are discussed for image formation.

1. When an object is at infinity

If the object is at infinity from the lens, the rays coming from the distant object are parallel to the principal axis. Therefore, after passing through the lens, they converge at the focus.