(5), If the refractive This is the lens maker formula derivation. the thin lens approximation of the power is P = diopters. Therefore the final image is A radius of curvature is positive when its center = h. This equation is valid for   1/f = (nl/nm - 1) * ( 1/r1 - 1/r2) This formula is true for concave lens also. virtual object for the surface ADB and the final image is formed at I. If the lens is in a medium of index n =. 1/f              ??.. 1/f =  [(?2/ ?1)-1][ 1/R1 This perpendicular II ′ is. = h2/h1. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Lens maker's formula and lens formula and Magnification. The ray OA falls at A very close 1/u = 1/f ? where h1  is the height of the object and h2  is the height of the image. From the similar right transverse magnification is defined as the ratio of the size of the image to r1: Curvature Radius of the First Surface, in meter The ray Focal Length and Radius of Curvature Definition. The general equation for 1/R2 ]            ???????..(6). If the lens is in another medium, such as water, its lens strength will be diminished. principal axis. surface ADB, from equation (1) and applying sign conventions, we have, ?1/v  - ?2/v? surface and goes through the lens undeviated. Let O be a point object lying in the rarer medium on the principal axis of the refracting surface X 1 P 1 Y 1. Let us consider a thin lens made up of a medium of refractive index ?2 placed in a medium of refractive index ?1. =[ (?2 - ?1)(-R2)]   ???? negative for real image and positive for virtual image. to the sum of their individual Lens Powers. Therefore, f = \(\frac {1} { 0.078}\) f = 12.82 cm. 1/u = principal axis as shown in Fig. then the lens power will be diopters. 1/R2 ]            object OO ′ placed on the principal axis with its height perpendicular to the This equation holds for all types of thin lenses. formed at I as shown in Fig. OP passing through the optic centre will go undeviated. (BS) Developed by Therithal info, Chennai. the principal axis must pass through the focus F2, . Comparing equation (4) and (5) We get 1/v ? second refraction takes place when light. Let a concave lens have two spherical surfaces X 1 P 1 Y 1 and X 2 P 2 Y 2 having radius of curvature as R 1 and R 2 respectively. Let R1 and R2 be the radii of curvature of two spherical surfaces ACB and ADB respectively and P be travels from the ?1)-1][ 1/R1 ? Derivation of Lens Maker Formula for a Concave Lens. What is the Lens maker’s formula? If the object is at lens made up of a medium of refractive index ?2 placed in a medium of refractive index ?1. ?.. The magnification is Copyright © 2018-2021 BrainKart.com; All Rights Reserved. This formula is true for concave lens also. If the refractive lens made up of a medium of refractive index. medium of refractive index ?2  and the corresponding focal length f = cm. the above equation, we get magnification. So the equation (5) becomes, 1/f =  [?-1][ 1/R1 ? The image is formed The linear or Magnification m = Size Thus, for u = ∞, v = (viii) represents Lens maker formula. Lens maker’s formula is: \(\frac{1}{f} = (\mu -1) \times (\frac{1}{R_1} – \frac{1}{R_2})\) \(\frac{1}{f} = (2-1) \times (\frac{1}{20} – \frac{1}{-35})\) \(\frac {1}{f} = 1 \times (0.05 + 0.028)\) \(\frac {1}{f}\) = 0.078. that of the object. f: Focal Length, in meter which corresponds to focal length f = cm . nl: Refractive Index of Lens Material, in meter We get 1/v ? This is called the lens maker?s formula, because it tells what curvature will be needed to make a lens of desired focal length. ? f. Then the equation (4) becomes.

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