Lens maker formula is used to construct a lens with the specified focal length. The medium on both sides of lenses should be the same. Derive an expression of a lens maker’s formula. Derivation . Draw image of an object. The incident rays make small angles with the lens surface or the principal axis. 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. Write the basic assumptions used in the derivation of lens – maker’s formula and hence derive this expression. Due to this reason, the separation between two of the refracting surfaces will also be small. Only the point objects are considered. The lenses should be thin. f = positive. The lens is thin and its distance measured from poles of surfaces can be considered as equal to the distance, from the optical center of the lens. (iii) The object is a point object and lies on the principal axis. (iv) The angle made by incident ray … Which of the following assumptions is NOT made in the derivation of Bernoulli’s equation. Derive an expression for lens-maker’s formula. This can be done, by making the ray optical calculation simpler, but at the first step, the constituents of thick and thin lenses should be identified. Basic assumptions in derivation of Lens-maker’s formula: (i) Aperture of lens should be small (ii) Lenses should be thin (iii)Object should be point sized and placed on principal axis. The following assumptions are taken for the derivation of lens maker formula. For different optical instruments, lenses having different focal lengths are used. Publish your article. Standing Waves in Strings and Organ Pipes. Consider a thin convex lens of focal length f and refractive index µ. The focal length of the lens is dependent on the radii of curvature and the refractive index of the lens. If the focal length is positive, then the lens is said to be converging, and if the focal length is negative, then it is said to be diverging. Here f represents the focal length, n is the refractive index of the material that is used to make the lens, R1 is the radius of the curvature of the first sphere, and R2 is the radius of curvature of sphere 2. Let us consider the thin lens with 2 refracting surfaces having the radii of curvatures R1 and R2 respectively. Assumptions for Derivation of Lens Maker’s Formula The lens is thin and its distance measured from poles of surfaces can be considered as equal to the distance, from the optical center of the lens. See also: Lens, Thin Lens Formula . (ii) Lenses should be thin. Formula. The lensmaker's equation relates the focal length of a simple lens with the spherical curvature of its two faces: , where and represent the radii of curvature of the lens surfaces closest to the light source (on the left) and the object (on the right). Let the refractive indices of the surrounding medium and the lens material be n1 and n2 respectively. For a Convex (converging) Lens; R1 = positive. Lensmaker Equation is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material and the surrounding medium. For a Concave (diverging) Lens; R1 = negative. The radii of curvature can be measured according to the cartesian sign convention. 1. Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Using Lens Makers formula, Derive thin lens formula. The lens maker’s formula can be described as below. Derivation It is used for determining the focal length of a thin lens (thickness = 0) with radii of curvature r1 and r2. 1 Answer. It is possible to ignore the double refraction if the optic’s lenses are thin enough for making the assumption that the light is refracted for only 1 time. The lens maker's formula can be derived for a concave lens in the same way. 1. (iii)Object should be point sized and placed on principal axis. 2. (ii) The aperture of the lens is small. The aperture of the lens is small. R2 radius is negative, as it is extending to the left side from the surface of the second one. Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures R1 and R2 respectively. Basic assumptions in derivation of Lens-maker’s formula: (iii)Object should be point sized and placed on principal axis. The sign of is determined by the location of the center of curvature along the optic axis, with the origin at the center of the lens.