# Concave Lens

## Introduction

In this tutorial, we will learn about concave lens. The image produced by the concave lens, the nature of the image formed, and ray diagrams related to the concave lens will be described in detail here.

Before proceeding further, let's recall some of the important points related to the concave lens.

• A concave lens diverges the incident rays.

• The diverged rays meet at a virtual point called Focus (F1) that exists on the opposite of the lens. The distance from Focus (F1) to Optical Centre (O) is called focal length (f1).

• A principal axis is a straight imaginary line consisting of optical center (O), Centre of Curvatures (C1 & C2), and radius of curvatures (R1 & R2).

• An aperture (A) is the linear diameter of the lens.

Now that you may have recalled the important points related to the concave lens, we will proceed further in this tutorial to understand the ray diagrams related to the concave lens.

## Ray Diagram: Concave Lens

### An Incident Ray Parallel to the Principal Axis

When an incident ray passes through a concave lens that is parallel to the principal axis, it gets refracted (or, diverged) away from the principal axis.

When a line from refracted ray is extended on the opposite side of the lens, it intersects the principal axis at a point. This point is referred to as virtual Focus and can be denoted as (F1).

Images coming soon

Image 1: An incident ray parallel to the principal axis

### Incident Ray appears to Intersect at Focus

When incident rays appear to be intersecting the Focus (F2) of a concave lens, it gets refracted parallel to the principal axis.

The incident ray can be extended by drawing a line on the opposite side of the concave lens. This extended line will intersect at the virtual Focus (F2).

Images coming soon

Image 2: Incident ray appears to intersect Focus (F2)

### Incident Ray on Optical Centre (O)

When an incident ray incident onto the Optical Centre (O) at any angle, it experiences no deviation (or, refraction) and normally crosses the Optical Centre (O). That is to say, there is no change in angle of refraction and no deviation from the original path occurs in the refracted ray.

Images coming soon

Image 3: Incident ray on Optical Centre (O)

## Image Formation: Concave Lens

Now that you may have completely understood the concept of ray diagrams of concave lens, let's proceed further to understand the image formation by concave lens. We will use our knowledge of ray diagrams of concave lens (learned in the previous section of this tutorial) to produce the images of an object placed at different points on the principal axis.

So, let's get started.

### Object placed at Infinity

When an object is placed at infinity, the incident rays from the object are parallel to the principal axis. According to the ray diagrams, the incident rays parallel to the principal axis diverges away from the principal axis on the opposite side.

When the diverged rays are extended with imaginary lines, the lines appear to be converge at the Focus (F1), as shown in figure below. The Focus (F1) lies on the same side of the concave lens. Hence, the image formed also lies on the same side of the lens.

Furthermore, the image formed is point-sized, virtual, and erect.

Images coming soon

Image 4: The object placed at infinity

### Object placed between Infinity and Optical Centre (O)

When the object is positioned somewhere between infinity and Optical Centre (O) of the concave lens, the image is formed between the Focus (F) and Optical Centre (O), as shown in the figure below. Image formation takes place on the same side of the concave lens.

An incident ray parallel to the principal axis gets refracted ways from the parallel axis on the opposite side of the concave lens. Additionally, another incident ray crosses the optical center (O) without any deviation.

When the diverged ray is extended by an imaginary line, it intersects the incident ray (passing through the optical center) and meets at Focus (F1). The distance between the point of intersection and the principal axis shows the size of the image formed as well as the position of the image.

Images coming soon

Image 5: Object between Optical Centre (O) and infinity

The nature of the image is virtual and erect. The size of the image is smaller than object.

### Object place between Optical Centre (O) and Focus (F)

When an object is placed between the Optical Centre (O) and Focus (F1), the image is formed between ‘O' and ‘F1'. The image is formed on the same side of the lens.

One incident ray parallel to the principal axis, gets deviated away from the principal axis. Upon extending the refracted ray, it meets at the Focus (F1). Also, another incident ray passing through the Optical Centre (O) does not deviate from its original path and crosses the ‘O' without changing the angle.

The point of intersection shows the image formation and size of the image formed, as shown in the image given below.

The nature of the image is virtual and erect. The size of the image is comparatively smaller than an object.

## Conclusion

Let's recall whatever we have learned in this tutorial so far. We learned about the ray diagrams of concave lenses. By applying the knowledge of ray diagrams, we learned how to obtain an image of the object placed at different positions on the principal axis of the concave lens.

Here is the table to summarize the image formation by a concave lens –

Object PlacedImage ObtainedNature of ImageSize of the image
At infinityAt Focus (F1) on the same side of lensVirtual + ErectPoint-sized
Between infinity and Optical Centre (O)Between Focus (F1) and Optical Centre (O) on same side of lensVirtual + ErectSmaller than object
Between Focus (F1) and Optical Center (O)Between Focus (F1) and Optical Centre (O) on the same side of lensVirtual + ErectSmaller than object

Table 1. Image Formation: Concave Lens

## FAQs

Q1. What a concave lens does?

Ans: A concave lens refracts the incident rays away from the principal axis. In other words, a concave lens diverges the incident rays. Also known as a divergent lens.

Q2. What makes a concave lens concave?

Ans: A concave lens diverges the incident rays because it is thicker at the edges and thinner at the middle part. Such a structure of its spherical surfaces, a concave lens becomes concave and diverges the incident rays.

Q3. Do concave lenses make images smaller?

Ans: Yes. The concave lenses make the images smaller in size than the objects.

Q4. What kind of image is formed by a concave lens?

Ans: A concave lens produces a virtual and erect image. Also, the size of the images is comparatively smaller than the size of the object.

Q5. What kind of lens is used by a short-sighted person?

Ans: Concave Lens. The concave lenses are used to rectify the short sight of a person. In myopia (short-sightedness) the image forms behind the retina. As a result, a person cannot see the image properly and gets a blurred vision. The concave lens diverges the incident rays from the object and allows the image formation to occur a little forward. This leads to the image formation exactly on the retina. Myopia can be corrected by a concave lens.