Derive lens formula for convex lens when virtual image is formed When parallel light from a source impinges on a converging lens, the parallel rays are refracted so that all the light comes f h or, f 1 = uh + vh = u1 + v1 This equation holds for both convex and concave lenses and for real and virtual images. Derivation of thin lens formula for a convex lens when it forms a virtual image As shown in figure, when an object AB is placed between the optical centre and focus of the convex lens, the image A. Aug 2, 2019 · Derive the lens formula, 1/f = 1/v - 1/u for a concave lens, using the necessary ray diagram. The object is a small object placed on the principal axis. To obtain this type of information it is necessary to use the lens equation and the magnification equation. An object is placed in front of a concave mirror. Figure 44. Hence, derive Lens Maker's formula. The lens formula is used to find image distance, type of image formed, and the focal length (f). Check more details like Formula, FAQs etc. What is the Derivation of Lens Makers Formula for Concave Lens? Newton’s Equation Let LL’ be a convex lens. A lens derive the relationship, 1/f = 1/u + 1/v for convex lens, where u is the object distance, v is the image distance and f is the focal length of the lens. Normally, one or both sides of the lens has a spherical curvature. 1. Thin Lens Formula with Magnification for Concave and Convex Lenses First, what is a thin lens? If the thickness of a lens is negligible in comparison to the radius of curvature, it is a thin lens. Jul 23, 2025 · The lens formula is an equation that explains how the object distance (u), image distance (v), and focal length (f) of a lens are related. Nov 5, 2020 · Thin Lens Equations for a Convex Lens: Shows how to use the thin lens equation to calculate the image distance, image height and image orientation for convex lenses when the object distance is greater the the focal length (f). if the object is kept between F1 and 0, the nature of the image will be virtual and erect whereas in all the other conditions the image formed by a convex lens will be 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 image distance can be calculated with the knowledge of object distance and focal length with the help of the lens formula. The nature of the image (real or virtual) depends on the type of lens and the position of the object. Hence derive lens maker's formula for a Article about Equation of converging (convex) lensWhen the beam of light passes through the focal point of the lens, the lens’s focal length is positive. The size of the image is smaller than that of the object. The equation is stated as follows: The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (h i) and object height (h o). Such images are formed with the simple magnifier . If there would have been a concave lens instead of the convex lens during derivation, the last part (where he uses sign convention on 1/f= 1/v + 1/u) the formula would have come out different (Since the object distance and the image distance both would have been negative in that scenario, the formula would have been 1/f = -1/v - 1/u). 1 The Thin-Lens Equation Lenses are common optical devices constructed of transparent material e. May 16, 2018 · (a) Obtain lens makers formula using the expression n 2 /v - n 1 /u = (n 2 - n 1)/R Here the ray of light propagating from a rarer medium of refractive index (n 1) to a denser medium of refractive index (n 2), is incident on the convex side of spherical refracting surface of radius of curvature R. Let us know the derivation of the lens formula. A concave lens is a lens that diverges a straight light beam from the source to a diminished, upright, virtual image. Jul 4, 2024 · Consider a convex lens of focal length f and optical centre C. An inverted magnified image A’B’ is formed as shown. Draw the ray diagram to show the image formation and hence derive the formula \frac {1} {v} + \frac {1} {u} = \frac {1} {f}. Draw a ray diagram for formation of image of a point object by a thin double convex lens having radii of curvature R1 and R2. The image distance can be Jun 10, 2025 · An example of the lens maker’s formula application is in the design of eyeglasses. Concave Lens is thinner in the middle and thicker at the edges. Images formed by these lenses can be real or virtual depending on their position from the lens and can have different sizes too. the image formation can be seen in two steps, the first refracting surface forms an image I 1 which acts as a virtual object for the second surface. What Is Lens Formula? Convex lenses are also known as converging lenses since the rays converge after falling on the convex lens, while concave lenses are known as diverging lenses as the rays diverge after falling on the concave lens. , left surface) and then use this image as the object for the second refracting surface. It uses similar triangles and algebraic manipulation to arrive at the formula \ [1/f = 1/d_0 + 1/d_i\], a key concept in optics for premed students. 4 cm in front of the concave lens (on its left side), Virtual and erect. Real image of a point light source is formed if physical rays actually meet after passing through the lens. Therefore, the focal length of the convex lens is 10. The difference in their behaviour is accounted for by using the correct To derive the thin-lens equation, we consider the image formed by the first refracting surface (i. formed by the lens is virtual, erect and magnified. Here, OF = OF’ = f; PF’ = x and QF = y; object distance, OP = -u = - (x + f) and OQ = v = y Image Formation by Lenses Virtual Image Formation Converging lenses form virtual images if the object distance is shorter than the focal length. This applies to all types of lens as long as the correct sign convention is used when substituting values for the distances. These lenses are used as per the requirement and play an important role in the study of optics. It has to be specified, the refractive index of the lens material, refractive index of the surroundings, and the radii The topic of Mirror Equation is important in physics and helps us understand how images are formed by different types of mirrors, such as concave and convex mirrors. Lens Formula for Convex Lens having virtual Image, Chapter 9, Ray Optics, Class 12 Physics Dynamic Vidyapeeth 508K subscribers Subscribe Sep 6, 2025 · Derivation of Lens Formula - The lens equation or lens formula is an equation that links the focal length, image distance, and object distance. As the object is brought closer to the convex lens from infinity to focus, the image moves away from the convex lens from focus to infinity. By using the lens maker’s formula, an optician can determine the appropriate curvature and material to create a lens with the precise focal length needed to correct the If a problem states that a real image is formed that is twice as large as an object, then you would use the relationship d = + 2d o in the thin lens equation. (i) Calculate the power of the new lens. Lens Formula for Convex Lens having Real Image, Chapter 9, Ray Optics, Class 12 Physics Dynamic Vidyapeeth 512K subscribers Subscribe When an object is placed at a finite distance from the lens, a virtual image is formed between the optical centre and the focus of the convex lens. A convex lens is a transparent optical element that curves outward on both sides and converges parallel rays of light to a single focal point. The formula is given by 1/f = 1/v - 1/u. The video also introduces the magnification formula for determining image height. 2. Learn about a lens's focal point and the thin lens assumption. Problem 4: The magnification of the mirror is -3 cm and the height of the object is 16cm then what is the length and nature of the image formed? May 28, 2024 · The lens formula helps in determining the nature, position, and size of the image formed by lenses. 5, the focal length of the lens (when used in air) will be Learn about the thin lens formula for concave and convex lenses, understand how to calculate magnification and explore FAQs related to lenses. (03marks) (b) Describe an experiment to determine the focal length of a convex lens fixed inside a short Derive lens maker formula for a convex lens. e. 2. By stating the sign convention and assumptions used, derive the relation between object distance u, image distance v and focal length f for a thin convex lens, when it forms real image of an object of finite size. All distances are measured from the optical center of the lens. Converging lenses concentrate parallel rays of light and diverging lenses cause parallel rays of light to spread out. A concave lens causes light rays to diverge before they strike the lens of the eye so that the image is formed on the retina. For a convex lens this happens if object is placed at a distance further than the first focal point of the lens. The figure above shows that the formation of a real, inverted and diminished image AB of the object AB placed beyond the centre of curvature at a distance u from the convex lens. Real-life Example Sep 20, 2020 · Lens Formula for Concave Lens having Virtual Image, Chapter 9, Ray Optics, Class 12 Physics Dynamic Vidyapeeth 498K subscribers Subscribed Lenses come into two general categories: converging (sometimes referred to as "convex") and diverging (sometimes referred to as "concave"). The nature of the image formed by a convex lens depends upon the position of the object. Key features include: Converging lens (thicker at the center) Made from glass or plastic Forms real or virtual images depending on object distance Commonly used in magnifying glasses, cameras, spectacles, microscopes Note : - We follow the sign convention for lenses In the image, the red text is negative, and blue text is positive Thus, If Virtual image is formed,v is negative If Real Image is formed, v is positive Object Distance (u) is always negative as it is on left side of the lens Focal Length of Convex Lens is Positive Focal Length of Concave Lens is The Lens Equation While ray diagrams can be used to determine the image location, size, orientation and type of the image formed by objects when placed at a given location in front of a lens, they will not provide numerical information about the image distance and size. The virtual image of this object A'B' is formed on the same side of the lens. Mar 20, 2025 · Understanding the mirror equation is essential in optics and physics, allowing us to predict the characteristics of images formed by mirrors, whether they are concave or convex. . An object of length ‘AB’ is held perpendicular to the principal axis beyond the focal length of the lens. B. Lens formula is a well-designed formula that is applicable for concave as well as convex lenses. The aperture of the lens is small. This formula works for both convex and concave lenses. Enter data below, then click on the quantity you wish to calculate in the active formula above. applying the equation above written for surface 1 This formula is widely used in both school-level physics, such as in lens makers formula class 10 and lens makers formula derivation class 12, as well as in professional lens design. the edges of the lens are curved outward rather than inwards. (a) Derive the mathematical relation between refractive indices n1 and n2 of two media and radius of curvature R for refraction at a convex spherical surface. The real object and real image distances are taken as positive distances. For a person with hyperopia (farsightedness), a convex lens is used to correct their vision by converging light rays onto the retina. To derive this formula we use the following sign conventions. (b) Light from a point Figure (a) shows the geometry of image formation by a double convex lens. The video provides a detailed walkthrough of deriving the lens formula, which relates the object distance, image distance, and focal length in a convex lens. Jul 23, 2025 · Hence, the image is formed at 2. The image is virtual, erect and is behind the object as shown in Fig. 52 shows the setup we will use to illustrate the method of finding location, size, and orientation of the real image. Using sign conventions, Let CB' = -v, CB When image formed is virtual When the object AB is placed between C and F, then the image formed by convex lens is virtual, erect and magnified as shown in the figure. A convex lens forms a real image when the object is farther from the lens than the focal length, causing light to converge at the focal length. The formula holds true for convex and concave lenses, regardless of whether the image is real or virtual. Nov 1, 2025 · A convex lens can form virtual as well as real images, so the magnification produced by a convex lens can be either positive or negative. Derivation formulas for lens essentially traces an arbitrary ray geometrically and mathematically from an object point through the two surfaces of a thin lens to the corresponding image point. It emphasizes how to determine whether these values are positive or negative based on the lens type (converging or diverging) and their positions. The focal point of the convex lens is passed through the beam of light. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. glass or plastic, which refract light in such a way that an image of the source of light is formed. It is observed that a virtual image is formed. Lens FormulaIt is a relationship between the focal length of a lens and distances of object and image from the optical center of the lens. (b) Draw a ray diagram to show the image formation by a concave mirror when the object is kept This video explains the thin lens formula and its components: focal length, object distance, and image distance. The image A1B1 is formed between O and F1 on the same side as the object is kept and the image is erect and virtual. F is the point of principal focus and ‘f’ is the point of focal length. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. Two lenses of power 10 D and −5 D are placed in contact. Using the common form of the lens equation, i is negative. Let an object AB be placed perpendicular to the principal axis at a point between C and F. g. (ii) Where should an object be held from the lens so as to obtain a virtual image of magnification 2? A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. The relationship between object distance, image distance, and focal length in lenses is described by the thin lens equation, which is a fundamental concept in optics. If a problem states that a virtual image is formed that is twice as large as the object, then you would use the relationship that d = − 2d o. Explore convex lenses, including how they refract and transmit light. Mar 26, 2025 · To derive the thin-lens equation, we consider the image formed by the first refracting surface (i. Both the incident and refracted rays make slight angles with the principal axis. (04marks) (ii) State three possible reasons under which an image of real object may not be formed by a convex lens on the screen. Magnification is positive for virtual image and negative for real image. Conversely, if the light beam does not pass the focal point of the lens, the focal length of the lens is negative. Real distances are taken as positive and virtual distances are tak Jun 17, 2019 · Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. 0 Assumption To Derive Thin Lens Formula The lens is thin. F, F’ and O are the second principal focus, the first principal focus and the optical centre of the lens respectively [Fig. ) For a treatment using waves and the curvature of the lens surface see Lenses and waves) Two proofs of the formula will be given here, one a geometrical proof and the other an optical version Jul 23, 2025 · Concave Lens is a diverging lens that scatters the incident light after refraction. Images formed by these convex lenses can be real or virtual depending on their position from the lens and can have a different size too. Thin Lens Equation A convex lens is a lens that converges the rays of light coming towards it. The sign convention used in the derivation of formula is All the distances are measured from the optical centre of the lens. Understanding the lens maker's formula for convex lens and concave lens allows you to predict how lenses will focus light and form images. A converging lens brings rays together at the focus, as at right, and can make either real or virtual images. ], P and Q are the point object and point image respectively. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index n1 and a real image formed in the denser medium of refractive index n2. The relationship between object distance, image distance, and focal length is crucial for various applications, from everyday situations to complex scientific instruments. If the object is placed between focus and optical center of the convex lens, erect and magnified image is formed. A certain biconvex thin lens is designed by drawing two circles of the same radius next to one another and using the overlapping region as the area to be used for the lens. This equation helps us understand how lenses form images and predict their size and location. Ans: Hint: For making a lens of desired focal length, the lens maker formula is used. When a ray goes through the optical centre of the lens, it passes without any deviation. If the radius of each circle is r, and the index of refraction of the glass for the lens is 1. Mirror Formula For Convex Mirror for Virtual Image, Chapter 9, Ray Optics, Class 12 Physics Dynamic Vidyapeeth 515K subscribers Subscribed The lens equation relates the object distance, the image distance and the focal length: we derive that equation here. Both types of lens can be used to form sharp images of an object. The following typical equation is used to determine a relation between the focal length of the lens, the distance of the object, and the distance of the image. The lens equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). 2. (Reminder: we use the 'real is positive, virtual is negative' sign convention. Derivation Of The Lens Formula: The above image is of a convex lens with an optical centre of O. This single formula applies to both convex (converging) and concave (diverging) lenses. What is the sign of the focal length for a concave lens? What type of images are formed by a concave lens? A concave lens forms virtual images, with negative image distance (v). The images formed by a concave lens are virtual and erect. jkwuv alca xjntf ltnpo yhsk qrgrlztwa nucf bhdv dqwb jptdf hri fhdkik ivlnx judzirgj lygprk