CI 1 = P 1 I 1 = V 1 (as the lens is thin) CC 1 = P 1 C 1 = R 1. But n2/n1 = n, relative refractive index of the lens w.r.t. Your email address will not be published. • CO = P 1 O = u. ∴                                                        – 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). 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. As previously mentioned, this equation can be used only for thin lenses. Saurabh Keshari. Hey Edubuzzer, welcome to the learning platform, EDUBUZZ NOTES. (ii) The aperture of the lens is small. The lens maker's formula can be derived for a concave lens in the same way. 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. Derivation of Lensmaker’s formula. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Now it is the situation, when the object is placed in the denser medium and image is formed in the rarer medium. the rarer medium. (i) All the distances are measured from the optical centre of the lens. Let O be a point object lying in the rarer medium on the principal axis of the refracting surface XP1Y. Then                                                    1/f – 1/∞ = (n – 1) (1/R1 – 1/R2), or                                                               1/f = (n – 1) (1/R1 – 1/R2), Your email address will not be published. Eqn. Performance & security by Cloudflare, Please complete the security check to access. Eqn. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. This is the lens maker formula derivation. or                                               – n2/v1 + n1/v= – (n2 – n1)/R2, or                                              – 1/u + 1/v = (n2/n1 – 1) (1/R1 – 1/R2). So I1 is the real image of the object O. Assumptions made to derive Lens maker formula : Derivation of Lens Maker Formula for Convex lens. 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. It follows from the refraction due to convex spherical surface XP 1 Y. So, I is the final virtual image of the object O. The ray diagram is as follows: Note: The lens maker's formula indicates that a convex lens can behave like a diverging one if m1 > m2 i.e., if the lens is placed in a medium whose m is greater than the m of lens. (iii) The object is a point object and lies on the principal axis. See also: Lens, Thin Lens Formula 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. This lens is bounded by two spherical refracting surfaces XP1Y and XP2Y. Derivation for lens makers formula . The point I1 acts as a virtual object placed in the denser medium for the spherical surface XP2Y. Another way to prevent getting this page in the future is to use Privacy Pass. Ray AB inside the lens will stiffer another refraction at surface X2 P2 Y2. Tags: Class 10 , Physics , Light Reflection Refraction Asked by Rah 1 Answers. Equation (v) is known as the lens makers formula. Let a concave lens have two spherical surfaces X1P1Y1 and X2P2Y2 having radius of curvature as R1 and R2 respectively. (viii) represents Lens maker formula. (i) The lens is thin and all the distances are measured from the optical centre of the lens. C1 and C2 be their centres of curvature and R1 and R2 be their radii of curvature respectively. Here at EBN, I write about Chemistry, Physics, Biology and Tips & Tricks. CD 2 = R 2. Derivation of Lens Maker Formula for a Concave Lens. 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. • Lens maker’s formula is: \(\frac{1}{f} = (\mu -1) \times (\frac{1}{R_1} – \frac{1}{R_2}) \) \(\frac{1}{f} = (2.5 -1) \times (\frac{1}{10} – \frac{1}{-12}) \) Derivation for lens makers formula . Derivation. It appears to come from point  I1 if the second surface X2P2Y2 were not present. (viii) represents Lens maker formula. 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. Cloudflare Ray ID: 5f99c1c71b971a2e So object lies in the rarer med1um, so we have, ∴                                                         – n1/u + n2/v1 = n2 – n1/R1      ……(i). In fact, the ray AB refracted by the first surface XP1Y is refracted at B by the second surface XP2Y and it finally meets the principal axis at I. This lens is placed in a medium of absolute refractive index n1 (n1 < n2 ). 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. I’m Imtiaz Ahmed, the learning guide from India. As B and D bothare close to the optical centre of the lens, BO = u, DI = +v, we obtain. 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