The incident rays make small angles with the lens surface or the principal axis. But this equation can only be used for the thin lenses. 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. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. 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. The lens maker’s formula can be described as below. 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. For a Convex (converging) Lens; R1 = positive. The aperture of the lens is small. A lens has two curved surfaces, but these are not exactly the same. If we know the refractive index and the radius of the curvature of both the surface, then we can determine the focal length of the lens by using the given lens maker’s formula: The lens maker’s equation is another formula and it gives the relationship between the radii of curvature, refractive index, focal length, of the two spheres that are used in the lenses. For different optical instruments, lenses having different focal lengths are used. The lenses, whose thickness is too less to be considered as negligible, as compared to the radius of curvature can be referred to as thin lenses. The ray diagram is as follows: Note: The lens maker's formula indicates that a convex lens can behave like a diverging one if m 1 > m 2 i.e., if the lens is placed in a medium whose m is greater than the m of lens. Consider a thin convex lens of focal length f and refractive index µ. Please contribute and help others. Lens maker’s formula is used by the lens manufacturers, for manufacturing of the lenses having the desired focal length. 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). The medium on both sides of lenses should be the same. See also: Lens, Thin Lens Formula . Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures R1 and R2 respectively. Lens maker formula is used to construct a lens with the specified focal length. The object lies close to principal axis. Standing Waves in Strings and Organ Pipes. Only the point objects are considered. 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. 1 Answer. Here is a deriation for lens makers formula: Assumptions. Draw image of an object. The focal length of the lens is dependent on the radii of curvature and the refractive index of the lens. 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. 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. The following assumptions are taken for the derivation of lens maker formula. (iv) The angle made by incident ray … Write the basic assumptions used in the derivation of lens – maker’s formula and hence derive this expression. 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. Similarly a concave lens can be made convergent. Suppose we have a thin lens of material of refractive index n2, placed in a medium of refractive index n1, let o be a point object placed on principle axis then for refraction at surface ABC we get image at I1 , ∴ (n2/v2) - (n1/u) = (n2 - n1 )/ R1 ....(1), But the refracted ray before goes to meet at I1 falls on surface ADC and refracts at I2, finally; hence I1 works as a virtual object 2nd refracting surface.