Lenses in Optics: Type, Uses, Solved Examples

Lenses: Lens is an optical device, that works on the principle of refraction of light and consists of a thin, transparent piece of glass or plastic that allows light rays to refract when passed through it. These light rays may converge or diverge after refraction. This lens property makes it a useful optical device that plays a very important role in our everyday lives. In this article, let us understand the concept of Lenses in detail. Read on to find out more.

What are Lenses?

Lenses are optical devices capable of transmitting light rays through them. Lenses are a transparent medium bounded by two curved surfaces which can refract light rays. A lens may have one surface plane and another surface spherical, which means that a lens is bounded by at least one spherical surface.

Lenses are usually made of a thin piece of glass or plastic.
For example, devices such as binoculars, telescopes, vision-correcting glasses, torches, and microscopes use lenses.

Definition: A lens is a thin piece of any transparent material like glass or plastic through which light can refract. This optical device is generally spherical in shape.

Lens Formula

The lens formula gives the relationship between the lens’s focal length, image distance, and object distance.
\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)
Where \(v\) is the image distance, \(u\) is the object distance, and \(f\) is the focal length of the lens.

Types of Lenses

There are two types of lenses depending on converging or diverging light rays. The two types of lenses are:

a. The convex lens (converging lens)
b. The concave lens (diverging lens)

Convex Lens

A convex lens has spherical surfaces which bulge out in the middle. A convex lens is thicker in the middle and thinner at the edges. This lens converges parallel rays of light falling on its surface. Therefore, a convex lens is also known as a converging lens. This lens can form both real and virtual images depending upon the object’s distance from the lens.

Concave Lens

A concave lens has a spherical surface that is curved inwards. A concave lens is thinner in the middle and thicker at the edges. A concave lens diverges parallel rays of light falling on its surface. Therefore, a concave lens is also known as a diverging lens. This lens constantly forms a virtual and erect image of an object irrespective of its distance from the lens.

Technical Terms Related to Lenses

1. Center of curvature: Each surface of a convex or concave lens forms a part of a sphere. The centre of this sphere is called the centre of curvature which is represented by the letter \(C.\) For a lens, there exists two centers of curvature that can be represented by \(C_{1}\) and \(C_{2}.\)
2. Principal axis: An imaginary line passing through the centres of curvature of a lens is called the principal axis of the lens.
3. Optical centre: A light ray passing through the optical centre of the lens never deviates from its path. The optical centre is located at the centre of the lens. It is represented by \(O.\)
4. Aperture of lens: The effective diameter of the circular outline of a lens is called the aperture of the lens.
5. Radius of curvature: The radius of the sphere from which the lens is taken out is called the radius of the lens. \(R_{1}\) and \(R_{2}\) are representing the radius of curvature of the lens.
6. Principal focus: For a convex lens, it is a point where all the parallel beams of light meet after refraction and for a concave lens, it is the point from where all the parallel beams of light appear to diverge after refraction.

Image Formation by Concave and Convex Lens

The refraction of light from a lens results in image formation. The formation of the image and the nature and position of the image formed by a lens can be represented by the ray diagram. We can draw the ray diagram by considering the rays to trace the path. We always need at least two such rays coming from the object and passing through the lens.

The point where the rays coming from the object meet or appears to meet after refraction gives the position of the image. To draw a ray diagram, we need to follow specific rules, which are given below:

1. A ray of light passing parallel to the principal axis after refraction from a convex lens pass through the focus. In the case of a concave lens, it appears to move away from stress so that when we extend the diverging ray, it will meet at the focus.
2. A ray of light passing through the optical centre will go without any deviation.
3. After refraction, a ray of light passing through the focus moves parallel to the principal axis for a convex lens. In the case of a concave lens, the ray of light appears to meet at the direction after refraction moves parallel to the principal axis.

Image Formation by Convex Lens

When an object \((AB)\) is kept at infinity, the rays of light falling on a convex lens appear to come parallel to the principal axis. Therefore, all these rays after refraction meet at the principal focus. This forms a real, inverted, and highly diminished image.

When an object \((AB)\) is kept at the centre of curvature, the image \((A’B’)\) will be obtained at the centre of the curvature on the opposite side of the lens. This image will be the same size as the object, real and inverted.

When an object \((AB)\) is kept between the focus and optical centre of a convex lens, the image \((A’B’)\) obtained will be on the same side of the lens where the object is kept. It will be virtual, inverted, and magnified.

Image Formation by Concave Lens

When an object is kept at infinity in front of a concave lens, the image will be obtained at the lens’s focus. This image will be highly diminished, virtual and erect.

Similarly, when the object \((AB)\) is placed between infinity and optical centre, the image \((A’B’)\) will form between the focus and optical centre of the concave lens. The image will be diminished, virtual and erect.

Sign Convention for a Lens

We can get the sign for each quantity used in the lens formula by applying the sign convention for a lens. According to sign convention, the optical centre is taken as the origin, and the principal axis acts as the X-axis. The convention rules are as follows:

1. The object is always placed to the left of the lens or optical center.
2. All distances parallel to the principal axis are measured from the optical center.
3. All distances measured to the right of the optical center or origin are taken as positive.
4. All distances measured to the left of the optical center or origin are taken as negative.
5. Vertical distances measured above the principal axis are taken as positive.
6. Vertical distances measured below the principal axis are taken as negative.

For example, the focal length of a concave lens is negative, and the focal length of a convex lens is positive.

Magnification for a Lens

Magnification for a lens is defined as the ratio of the height of the image to the size of the object. It is denoted by the letter \(‘m’.\) It is equal to the ratio of the image distance to the object distance.
\(m=\frac{h^{\prime}}{h}=\frac{v}{u}\)
Where \(v=\) Image distance from the lens
\(u=\) Object distance from the lens
\(h’ =\) Height of the image
\(h=\) Height of the object

Uses of Lenses

Depending on the image type formed by different lenses, we can use lenses in many applications. The convex lens gives a virtual, erect, and highly magnified image of an object when it is kept very close to it. So, it can be used as a magnifying glass, whereas a concave lens constantly forms virtual and diminished images, so we can use it at the places where we need a wider field of view.

Uses of Convex Lens

• (i) A convex lens is used to correct hypermetropia.
• (ii) A convex lens is used in projectors and microscopes.

• (iii) A convex lens is used by ENT doctors to get a magnified image of an object.

Uses of Concave Lens

1. A concave lens is used to correct myopia.
2. A concave lens is used in peepholes in doors.
3. A concave lens is used in lasers for widening their beam.

Uses of Lenses

Solved Examples – Lenses

Q.1. An object \({\rm{5}}\,{\rm{cm}}\) in length is held \({\rm{25}}\,{\rm{cm}}\) away from a converging lens of focal length \(10\,{\rm{cm}}{\rm{.}}\) Find the position, size and nature of the image formed.
Sol: Given, The radius of curvature, \(f = 10\,{\rm{cm}}\)
The object distance, \(u = -25\,{\rm{cm}}\)
The height of the object, \(h = 5\,{\rm{cm}}\)
The height of the image \(= h’\)
Using lens formula, \(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)
\(\Rightarrow \frac{1}{v}=\frac{1}{10}-\frac{1}{25}=\frac{3}{50}\)
The image distance, \(v = 16.7\,{\rm{cm}}\)
From this, it is clear that the image is real and formed at a distance of \(16.7\,{\rm{cm}}{\rm{.}}\)
Magnification, \(m=\frac{h^{\prime}}{h}=\frac{v}{u}=\frac{16.7}{-25}=-0.668\)
Since magnification is negative, the image will be inverted.
Height of image, \(h’ = mh = \, – 0.668 \times 5 = \, – 3.34\,{\rm{cm}}\)
Therefore, the image formed will be real, inverted and diminished

Q.2. A concave lens has a focal length of \(15\,{\rm{cm}}{\rm{.}}\) At what distance should the object from the lens be placed so that it forms an image at \(10\,{\rm{cm}}\) from the lens?
Sol: A concave lens forms a virtual and erect image of the object. This image will be formed on the same side of the object.
Given, the image distance, \(v = \, – 10\,{\rm{cm}}\)
The focal length of the lens, \(f= \, – 15\,{\rm{cm}}\)
Let the object distance be \(u.\)
By applying the lens formula, we will get
\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)
\(\Rightarrow \frac{1}{u}=\frac{1}{v}-\frac{1}{f}\)
\(\Rightarrow \frac{1}{u}=\frac{1}{-10}-\frac{1}{(-15)}=\frac{1}{-10}+\frac{1}{15}\)
\(\Rightarrow \frac{1}{u}= -\frac{1}{30}\)
\(\Rightarrow u = \, – 30\,{\rm{cm}}\)
Therefore, the object should be placed at \(30\,{\rm{cm}}\) from the concave lens.

Related topics to Lens

Summary

From this article, we learned that lenses, transparent optical devices of various spherical shapes, can refract light in many ways. We can get real and virtual images of different sizes depending upon the distance of the object from a particular lens. A convex or converging lens acts as a magnifying glass, whereas a concave or diverging lens gives a wider field of view.

FAQs on Lenses

Here are some of the most asked questions related to Lenses:

Q.1. What are the three types of lenses?
Ans: A convex lens is of three types: a bi-convex or double convex lens, a plano-convex lens, and a concave-convex lens. A concave lens is also of three kinds: bi-concave or double-concave lens, plano-concave lens, and convexo-concave lens.

Q.2. What is meant by a lens?
Ans: Lens is an optical device capable of transmitting light rays through it. The lens is a transparent medium bounded by two curved surfaces which can refract light rays.

Q.3. What do lenses do?
Ans: Lenses are optical devices capable of refracting light in many ways depending upon its thickness. They converge or diverge light rays from an object to give an image that can be real or virtual. This property of lenses is used in many applications, such as magnification.

Q.4. What are the types of lenses?
Ans: There are two types of lenses depending on their ability to converge or diverge light beams. They are convex lens and concave lens. A concave lens can diverge light rays, whereas a convex lens converges the light rays falling on its surface.

Q.5. What is the formula for a lens?
Ans: The lens formula gives a relationship between the image distance \((v),\) object distance \((u)\) and the focal length \((f)\) of the lens. It is given by
\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

We hope the topics covered in this article about the lens in optics have helped you understand the concept in detail. However, if you have any queries on the lens, ping us through the comment box below, and we will get back to you as soon as possible.