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. Either form can be used with positive or negative lenses and predicts the formation of … 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. 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 Derivation. Get your confusion cleared by going through the post on this site here. The sign convention should be followed in the application of the lens maker’s equation. A common Gaussian form of the lens equation is shown below. Thin Lens Equation. So we can conclude that a convex lens need not necessarily be a converging and a concave lens diverging. Thus, 1 f = (n −1) 1 R1 + 1 R2 , (9) which is the lensmaker’s formula. Next plug in n1 for the type of water, fresh or ocean. 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). You would use his prescription in diopters (1/m) to replace 1/f. A form using the Cartesian sign convention is often used in more advanced texts because of advantages with multiple-lens systems and more complex optical instruments. 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. Assumptions. See also: Lens, Thin Lens Formula This is the form used in most introductory textbooks. A lens is said to be thin if the gap between the two surfaces is very small. Lens manufacturers commonly use the lens maker formula for manufacturing lenses of the desired focal length. Learn lens makers formula. Multiple Choice Questions involving Lens Maker’s Equation While attempting to solve problems in optics related to spherical mirrors and lenses, many among you will have some confusion about the application of the inevitable sign convention. Focal Length and Radius of Curvature Definition When parallel light rays are incident on a lens, the refracted rays converge to a point (for a converging lens) or appear to diverge from a point (for a diverging lens). A lens will be converging with positive focal length, and diverging if the focal length is negative. This is the lens makers equation… Let's say you are making a prescription glass face plate for a scuba diver.

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