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Thin Lens Formula for Concave and Convex Lens

Last updated date: 17th May 2024
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Thin Lens formula for Concave and Convex Lenses

In this section, the students will learn about the Concave and Convex Lenses, their uses in different ways, the formula for the same, and other concepts. The students can learn more such concepts from Vedantu’s website for free of cost. The resources available can be downloaded in PDF format for their reference or can also be viewed online.


What is Thin Lens?

A thin Lens is nothing but such Lenses whose thickness is negligible when compared to their Radii of Curvature. To gain a better insight into the thin Lens, refer to this diagram below

Before understanding the Concave and Convex Lens formula, take a look at Figure 1.0. Here, thickness (t) is much smaller than the two Radii of Curvature R1 and R2.


Convex Lens

A curved transparent medium that is made up of glass and looks like a part of a compact sphere is known as a Convex Lens. The surface of the Convex Lens has an external curve that looks like the surface of a glass ball. So, when the light rays fall on the Convex surface of the Lens, they tend to converge from their paths and when both the surfaces are Convex, they are known as biConvex Lenses, and when one surface is plane and the other is Convex, it is a plano-Convex Lens. However, the behaviour of the Lenses depends on the degree of the Curvature of a Convex Lens. So, when parallel rays fall on the Convex surface of this Lens, they converge and meet at a single point which is called the focus of the Lens.


Uses of a Convex Lens

Convex Lenses are used majorly in microscopes, magnifying glasses, and eyeglasses. They are also used in cameras to create real images of objects that are present at a distance and the nature of the image depends on the way these Lenses are used, however, the prime reason for learning the uses of Convex Lenses is to find the use of light refraction to see things properly.


It is a type of transparent medium that is made of glass which contains one or two Concave surfaces. The best way to identify a Concave Lens is by checking the curved surface as it resembles the inner surface of a hollow sphere, just like the mouth of a cave. These are also known as divergent Lenses as the parallel beams incident on their surface tends to diverge from their paths.


These Lenses can never produce a real image as their property is to diverge light rays away from their path which means in simple words that the light rays will not converge and meet at a point physically. So, when the rays are produced backwards in a virtual way, they meet at a point and this is the prime difference between a Concave and a Convex Lens.


Uses of a Concave Lens

A Concave Lens is used to diverge incident rays as this helps to create a virtual image on the opposite side of the refracting surface. Therefore, these Lenses are used in binoculars, telescopes, cameras, flashlights, and eyeglasses. These images are erect and upright, unlike the real images. And this is the basis for distinguishing between Concave and Convex Lenses by learning the features of light rays refracting inside the Lenses.


Lens Formula for Concave Lens and Convex Lens

For such a Lens, Focal Length, image distance and object distance are interconnected. One can establish this connection, by the following formula – 

1/f = 1/v + 1/u

In this equation, f is the Focal Length of the Lens, while v refers to the distance of the formed image from the Lens’ Optical Centre. Lastly, u is the distance between an object and this Lens’ Optical Centre. This is the Lens equation for Convex Lenses.


Two Types of Thin Lens

To derive a thin Lens formula, you must first understand that Lenses can be of two types – converging and diverging.

  • Converging – These are Lenses where light rays parallel to the optic axis pass through and converge together at a common point behind them. This point is known as the Focal point (f) or focus.

  • Diverging – These Lenses perform a contrasting function to that of Converging Lenses. Here, the rays of light parallel to the Optic Axis pass through it and Diverge. It gives rise to an optical illusion, making it feel as if the lights come from the same source (f) in front of the Lens.


Characteristics of Thin Lens Image Formation

Simply knowing the thin Lens formula for Convex Lenses is not enough. You must understand the characteristics of a ray of light passing through converging and diverging Lenses.

  • Parallel rays passing through converging Lenses will meet at point f on the other side.

  • Parallel rays entering diverging Lenses seem to arise from point f in front of it.

  • Light rays passing through the centre of converging or diverging Lenses do not change their directions.

  • Light rays entering a converging Lens through its Focal point will always exit parallel to its axis.

  • A light ray heading towards the Focal point on the other side of a diverging Lens will also come out parallel to its axis.

Focal Length is negative for a Concave or diverging Lens. Similarly, the image distance is negative when the image is formed on the side where the object is placed. In such an event, the image is virtual. Positive Focal Length, on the other hand, denotes a converging or Convex Lens.


Multiple Choice Question

Which of the following is true?

  1. Lens power is always negative

  2. Lens power is always positive

  3. The power of the Concave Lens is positive

  4. The power of the Convex Lens is positive

Ans: (d) The power of Convex Lens is positive


Thin Lens Formula for Lens in Contact

Now that you are aware of the Focal Length of the Convex Lens formula, you should assess the combination of thin Lenses in contact. If two such Lenses are in contact, the formula to determine the combined Focal Length is,

1/f = 1/f1 + 1/f2

Here, f is the combined Focal Length, while f1 is the Focal Length of the first Lens and f2 is the Focal Length of the second Lens. Therefore, for n number of Lenses, the Focal Length is

1/f = 1/f1 + 1/f2 + 1/f3…. + 1/fn 

Convex Lens formula is a crucial part of your Physics curriculum. Assistance from world-class teaching staff and online classes can help you get a better grasp of this concept. Now you can download our Vedantu app and have easy access to study material on related topics, as well as online classes from professional teachers.

FAQs on Thin Lens Formula for Concave and Convex Lens

1. What is the Lens Formula for Convex Lens?

According to the Convex Lens equation, 1/f = 1/v + 1/u. It relates the Focal Length of a Lens with the distance of an object placed in front of it and the image formed of that object. In other words, it can be considered as an extended object AB which is placed in front of a Convex Lens. Now, let O be the optical centre of the Lens. So, when the object AB is held close to the Lens between O and F the image A'B' formed by the Convex Lens is virtual, erect, and magnified or, 1/f = 1/v + 1/u is the required equation.

2. When is Image Virtual for a Concave Lens?

The image formed from a Concave Lens is virtual only when the object and image are on the same side of the Lens. In simple words, a Concave mirror or a converging Lens only produces a virtual image at a point, if the image is located beyond the Focal point which means the point that is more than one Focal Length away. Here, the image that will be formed will be upright and reduced in size since it is formed by a Concave Lens.

3. When do Combined Lenses Behave as Convex Lenses?

If the Focal Length of the second Lens is greater than the first Lens’ Focal Length, the resulting combined Lens acts as a Convex Lens. So, when two Lenses are used in combination, the first one forms an image that serves as the object for the second Lens. While the magnification of the combination is the ratio of the height of the final image to the height of the object. Therefore, combined Lenses behave as Convex Lenses when the Focal Length of the first Lens is less than the second one.

4. When do Concave Lenses behave as Convex Lenses?

As we all know by now that Convex Lenses are diverging Lenses and Concave Lenses are converging Lenses, so, let us further deep dive into the concept. So, a Convex Lens behaves as a Concave Lens and vice versa is also true when they are placed in a liquid of refractive index that is greater than the refractive index of the Lens. For more such concepts the students can visit the website of Vedantu and avail themselves of these resources for free.

5. Why are the glasses Convex in nature?

The Convex Lenses are used in eyeglasses for correcting the farsightedness of the viewer, where the distance between the eye's Lens and the retina is too short, due to which the Focal point lies behind the retina. Thus, eyeglasses with Convex Lenses increase refraction and accordingly reduce the Focal Length of the surface. The glasses are Convex for the Focal point Length. The students can get the resources related to these topics from the website of Vedantu free of cost.