Derivation for lens makers formula . Tags: Class 10 , Physics , Light Reflection Refraction Asked by Rah 1 Answers. Consider a convex lens with O be the optical centre, and F be the principal focus with focal length f. Now, let AB be the object kept perpendicular to the principal axis and at a distance beyond the focal length. Now using this I have to derive Lens makers Formula… Derivation of Lens Formula for concave lens: Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. ; The lens has a small aperture. 2. For the past 1 hour, I’m trying to derive lens maker’s equation using fermat’s principle, which of course is our homework. Any help would be great regarding the topic. The image A 1 B 1 is formed between O and F 1 on the same side as the object is kept and the image is erect and virtual. 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. applying the equation above written for surface 1 Thus, 1 f = (n −1) 1 R1 + 1 R2 , (9) which is the lensmaker’s formula. 1. 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. The thin lens equation is also sometimes expressed in the Newtonian form. The derivation of the Gaussian form proceeds from triangle geometry. the image formation can be seen in two steps, the first refracting surface form an image I 1 which act as a virtual object for the second surface. Here, x 1 and x 2 are the distances to the object and image respectively from the focal points. The Newtonian Lens Equation We have been using the “Gaussian Lens Formula” An alternate lens formula is known as the Newtonian Lens Formula which can be easily verified by substituting p = f + x 1 and q = f + x 2 into the Gaussian Lens Formula. Numerical Methods In Lens (A) Lens Formula Definition: The equation relating the object distance (u), the image distance (v) and the focal length (f) of the lens is called the lens formula. According to Fermat’s Principle, optical path length OPL = PA + AQ, here PA and AQ are two rays. For thicker lenses, Gullstrand's equation can be used to get the equivalent power. For a thin lens, the lens power P is the sum of the surface powers. The object lies close to principal axis. Considering the approximations used, we should not expect this formula … Assumptions made: The lens is thin. Figure (a) shows the geometry of image formation by a double convex lens. Lens Formula Derivation. Convex Lens. ; The incident rays make small angles with the lens surface or the principal axis.
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