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# Concave lens, terminology, Image formation, Lens formula, Practice problems, FAQs

When a human can clearly see objects that are near only, but objects farther away are blurry, it is a defect in eyes known as short-sightedness or myopia. In this defect the eye focuses the light rays before the back of the eyeball. To correct this defect we generally use a lens known as concave lens, this lens pushes the light rays further apart so that they arrive in proper focus at the back of the eye. You can see in figure how the concave lens is focusing the rays at the back of the eyeball.

Now let's understand the concave lenses in detail.

Table of content

• Introduction
• Key terms for Concave Lenses
• Image Formation in Concave Lens
• Lens formula for concave lens
• Practice problems
• FAQs

## Introduction

A concave lens is a transmissive optical device that disperses a light beam by the means of refraction.

A concave lens is made up of two concave surfaces, which are also a part of two spheres as shown in the figure.

The concave lenses are thick at the edges and thin in the middle. These lenses have a property to diverge the light that falls on its surface. Therefore, they are also known as the diverging lenses.

The various types of diverging lens are as shown in figure.

## Key terms for Concave Lenses

1. Center of curvature: The center of the sphere from which a concave lens is formed is known as the center of curvature. In the figure, C1 and C2 are the centers of curvature.

2. Radius of curvature: The radius of the sphere from which the concave lens is formed is known as the radius of curvature.
3. Optical center: The central point of the lens through which a ray of light passes without any deviation is k
own as the optical center. In the figure, the optical center is denoted by O.

4. Principal axis: The principal axis is the line joining the optical center to the centers of curvature.

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

First principal focus:

For a concave lens, it is the point on the principal axis towards which when the light rays come, they become parallel to the principal axis after passing through the lens.

Second principal focus

For a concave lens, it is the point on the principal axis on which the rays parallel to the principal axis appear to meet 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.

## Image Formation in Concave Lens

For a concave lens, in the first case, an object is at infinity. In the second case, an object is placed anywhere in front of the lens.

1. When an object is at infinity

When the object is at infinity, the rays from the object are parallel to the principal axis. On retracing back, the emerging rays seem to meet at the focus.

The characteristics of the image formed are as follows:

1. The image is formed at the focus.
2. The image formed is virtual and erect.
3. The image formed is highly diminished.

2. When an object is placed anywhere on the principal axis

In this case, the image formed is always between the focus and the optical center.

The characteristics of the image formed are as follows:

1. The image is formed between F and the optical center.
2. The image formed is virtual and erect.
3. The image formed is diminished.

Lens formula for concave lens

To find the the position of image for the various distance of object we use lens formula which is given as

Where,

v = x-coordinate of the image

u = x-coordinate of the object

f = focal length

Sign convention:  The direction of the incident ray is taken as positive and optical center as origin. For concave lenses f is negative

## Practice problems

Q 1. A concave lens focuses an image 20 cm from the lens of an object at a distance 30 cm from the lens. Find the focal length of the lens.

Given : u=-30 cm

v=-20 cm

Using lens formula

Focus of a concave lens is always negative.

Q 2. An object is placed 50 cm from a concave lens of focal length 20 cm, find the position and nature of the image.

Given :

For concave lens focal length will be negative, hence f=-20 cm

u=-50 cm

Using lens formula

Image will be virtual and erect.

Q 3. A concave lens having focal length 15 cm forms an image at a distance 10 cm from the lens. How far should the object be placed from the lens?

Given :

We know concave lens has negative focal length, hence f=-15 cm

v=-10 cm

Using lens formula

Hence the object should be placed at 30 cm in front of the lens.

Q 4. An object situated at 60 cm from a lens gives a virtual image at 20 cm in front of the lens. What is the focal length of the lens? What type of lens is it?

Given : u=-60 cm

v=-20 cm

Using lens formula

f=-30 cm

Because the focal length is negative, so the lens is concave lens.

## FAQs

Q1. Which lens is used in torch lights?
Answer: Concave lens is used because it spreads the light rays and produces a broader range of light.

Q 2. Write any two rules for obtaining an image formed by a concave lens?

1. Ray of light parallel to the principal axis appears to have passed through the focus after refraction through the lens.
2. A ray of light which passes through the optical center of the concave lens does not bend after refraction and goes straight.

The intersection of the above two rays after refraction gives an image.

Q 3. What happens to the degree of refraction if the concave lens is placed in water?
Answer: Relative Refractive index between water and glass is smaller than air and glass, so the light ray will be bent by a smaller amount after refraction.

Q 4. Why can't real images form by concave lens?
Answer: Since the rays passing through the concave lens diverge and do not meet at any point.

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