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?
Lens power is always negative
Lens power is always positive
The power of the Concave Lens is positive
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 Thin Lens Formula, and is it the same for both concave and convex lenses?
The Thin Lens Formula is a fundamental equation in optics that relates the focal length (f) of a lens to the distance of the object (u) and the distance of the image (v) from the optical centre. The formula is given by 1/f = 1/v - 1/u. This single formula applies to both convex (converging) and concave (diverging) lenses. The difference in their behaviour is accounted for by using the correct sign conventions for f, v, and u.
2. What are the Cartesian sign conventions used for the thin lens formula?
The Cartesian sign conventions are crucial for correctly applying the thin lens formula. As per the CBSE/NCERT 2025-26 syllabus, the standard conventions are:
- The optical centre (O) of the lens is treated as the origin (0,0).
- All distances are measured from the optical centre.
- Distances measured in the same direction as incident light are considered positive.
- Distances measured in the opposite direction to incident light are considered negative.
- Heights measured upwards and perpendicular to the principal axis are positive.
- Heights measured downwards and perpendicular to the principal axis are negative.
3. Why is the focal length of a convex lens considered positive, while that of a concave lens is negative?
This is a direct result of the sign conventions. For a convex lens, parallel rays of light converge at the principal focus (F) on the opposite side of the lens. Since this distance is measured in the direction of the incident light, its focal length (f) is positive. For a concave lens, parallel rays diverge and appear to come from a principal focus on the same side as the object. Since this distance is measured against the direction of incident light, its focal length is negative.
4. What is the primary difference between the image formed by a convex lens and a concave lens for a real object?
The primary difference lies in the nature of the image formed. A concave lens always forms a virtual, erect, and diminished image for any position of a real object. In contrast, a convex lens can form different types of images depending on the object's position. It can form a real, inverted image (of varying sizes) or a virtual, erect, and magnified image when the object is placed within its focal length.
5. What are the key assumptions made for the thin lens formula to be valid?
The derivation and application of the thin lens formula (1/f = 1/v - 1/u) rely on a few key assumptions. These are important to understand for its correct application:
- The lens must be 'thin', meaning its thickness is negligible compared to the object distance, image distance, and radii of curvature.
- The object must be a point object situated on the principal axis.
- The aperture of the lens (its effective diameter) must be small to minimise aberrations.
- The rays of light considered are paraxial, meaning they are close to the principal axis and make small angles with it.
6. How is the magnification of an image calculated using the thin lens formula?
Linear magnification (m) produced by a lens describes the ratio of the image height (h') to the object height (h). It also relates to the image distance (v) and object distance (u). The formula is m = h'/h = v/u. A positive value of 'm' indicates a virtual and erect image, while a negative value indicates a real and inverted image. An absolute value of 'm' greater than 1 means the image is magnified, while a value less than 1 means it is diminished.
7. What happens to the thin lens formula when two thin lenses are kept in contact?
When two thin lenses with focal lengths f₁ and f₂ are placed in contact, they behave as a single equivalent lens. The focal length (F) of this combination is given by the formula: 1/F = 1/f₁ + 1/f₂. The power of the combination is the algebraic sum of their individual powers (P = P₁ + P₂). This principle is essential in designing complex optical instruments like cameras and microscopes where multiple lenses are used to correct aberrations and achieve desired magnification.
8. Under what condition can a converging (convex) lens behave like a diverging (concave) lens?
A convex lens, which normally converges light, can behave like a diverging lens if it is placed in a medium with a refractive index greater than the refractive index of the lens material itself. According to the Lens Maker's Formula, the focal length depends on the refractive indices of both the lens and the surrounding medium. When the surrounding medium is optically denser, the nature of the lens inverts, causing it to diverge parallel light rays instead of converging them.
