Assumptions made to derive Lens maker formula : (i) The lens is thin and all the distances are measured from the optical centre of the lens. (viii) represents Lens maker formula. Let O be a point object lying in the rarer medium on the principal axis of the refracting surface X1P1Y1. This lens is bounded by two spherical refracting surfaces XP1Y and XP2Y. Similarly a concave lens can be made convergent. (iv) The angle made by incident ray and refracted ray with the principal axis are small. Therefore,equation (iv) can be written as. Derivation of Lens Maker Formula for a Concave Lens. Writing the lens equation in terms of the object and image distances, 1 o + 1 i = 1 f. (8) But o1 and i2 are the object and image distances of the whole lens, so o1 = o and i2 = i. Saurabh Keshari. Another way to prevent getting this page in the future is to use Privacy Pass. You may need to download version 2.0 now from the Chrome Web Store. So I1 is the real image of the object O. This lens is placed in a medium of absolute refractive index n1 (n1 < n2 ). The Lens Maker’s Equation for Thin Lenses: where, f is the focal length (half the radius of curvature) n is the refractive index of the material used. C1 and C2 be their centres of curvature and R1 and R2 be their radii of curvature respectively. The formula giving the relation between the focal length (f) of the lens, the refractive index of the material of the lens (n) and the radii of curvature of its surface (R1 & R2) is known as Lens maker formula. The point I1 acts as a virtual object placed in the denser medium for the spherical surface XP2Y. SF017 SF027 51 1.5 Thin Lenses Formula and Lens maker’s Equation {Considering the ray diagram of refraction for 2 spherical surfaces as shown in figure below. or – n2/v1 + n1/v= – (n2 – n1)/R2, or – 1/u + 1/v = (n2/n1 – 1) (1/R1 – 1/R2). (iii) The object is a point object and lies on the principal axis. (iv) The angle made by incident ray … Cloudflare Ray ID: 5f99c1c71b971a2e Since object lies in the rarer medium, so we have. Applicable for both the convex and concave lenses, the lens formula is given as: 1/v - 1/u = 1/f Where, v = Distance of image formed from the optical center of the lens. Performance & security by Cloudflare, Please complete the security check to access. I’m Imtiaz Ahmed, the learning guide from India. Let O be a point object lying in the rarer medium on the principal axis of the refracting surface XP1Y. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. So, I is the ﬁnal virtual image of the object O. (i) The lens is thin and all the distances are measured from the optical centre of the lens. The lens maker's formula can be derived for a concave lens in the same way. Assumptions made to derive Lens maker formula : Derivation of Lens Maker Formula for Convex lens. Thus, 1 f = (n −1) 1 R1 + 1 R2 , (9) which is the lensmaker’s formula. Considering the approximations used, we should not expect this formula … The lens is assumed to be constructed of a substance with a refractive index of n. The medium in which the lens is immersed is air with a refractive index of 1. Equation (v) is known as the lens makers formula. Point I1 acts as the virtual object placed in the denser medium for the surface X2P2Y2. • Hey Edubuzzer, welcome to the learning platform, EDUBUZZ NOTES. For u = infinity, the image is formed at principal focus so v = f (the focal length of the lens). CI 1 = P 1 I 1 = V 1 (as the lens is thin) CC 1 = P 1 C 1 = R 1. After refracting from surface X2P2Y2, the ray travels along BD and appears to come from the point I. Using the formula for refraction at a single spherical surface we can say that, For the first surface, For the second surface, Now adding equation (1) and (2), When u = ∞ and v = f. But also, Therefore, we can say that, Where μ is the refractive index of the material. It follows from the refraction due to convex spherical surface XP 1 Y. This is the lens maker formula derivation. Therefore I is the final real image of O. Lens makers formula: It is a relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. Derivation for lens makers formula . (i) All the distances are measured from the optical centre of the lens. So I1 is the virtual image of the object O. Using the positive optical sign convention, the lens maker's formula states {1\over f} = (n-1)\left({{1\over R_1} - {1\over R_2}}\right) where f is the focal length, n is the index of refraction, and R_1 and R_2 are the radii of curvature of the two sides of the lens. R2 is the radius of curvature of sphere 2. • Ray AB inside the lens will stiffer another refraction at surface X2 P2 Y2. Here the object distance is. Eqn. As B and D bothare close to the optical centre of the lens, BO = u, DI = +v, we obtain. or 1/f = (n – 1) (1/R1 – 1/R2). C is the optical centre of the lens. (ii) Distances measured in the direction of the propagation of incident light are taken as positive while the distances measured in the direction opposite to the direction of propagation of incident light are taken as negative. Eqn. Tags: Class 10 , Physics , Light Reflection Refraction Asked by Rah 1 Answers. The manufacturers of the lenses use this relation to design the lens of a given focal length and hence it is called so. BC 1 =R 1. As per optical physics, lens formula relates the distance of an object (u), the distance of an image (v), and the focal length (f) of the lens. O C 1 II C 2 1 P 1 P 2 I2 B E A D u1 v1 v2 r1 r2 t n1 t −v1 n2 n1 SF027 52 {By using the equation of spherical refracting surface, the refraction by first surface AB and second surface DE are given by But n2/n1 = n, relative refractive index of the lens w.r.t. Your email address will not be published. If the object is at infinity, the image is formed at the principal focus of the lens. ∴ – n2/v1 + n1/v = n2 – n1/- R2, or 1/v – 1/u = (n2/n1 – 1) (1/R1 – 1/R2), or 1/v – 1/u = (n – 1) (1/R1 – 1/R2) (n2/n1 = n).

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