Lens Formula Derivation. 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 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. According to Fermat’s Principle, optical path length OPL = PA + AQ, here PA and AQ are two rays. Convex Lens. 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. applying the equation above written for surface 1 2. 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. 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. Figure (a) shows the geometry of image formation by a double convex lens. For the past 1 hour, I’m trying to derive lens maker’s equation using fermat’s principle, which of course is our homework. Derivation for lens makers formula . Any help would be great regarding the topic. Here, x 1 and x 2 are the distances to the object and image respectively from the focal points. For thicker lenses, Gullstrand's equation can be used to get the equivalent power. 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. Now using this I have to derive Lens makers Formula… The object lies close to principal axis. ; The incident rays make small angles with the lens surface or the principal axis. 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. 1. The derivation of the Gaussian form proceeds from triangle geometry. Assumptions made: The lens is thin. ; The lens has a small aperture. The thin lens equation is also sometimes expressed in the Newtonian form. 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. For a thin lens, the lens power P is the sum of the surface powers. Tags: Class 10 , Physics , Light Reflection Refraction Asked by Rah 1 Answers. Considering the approximations used, we should not expect this formula … Thus, 1 f = (n −1) 1 R1 + 1 R2 , (9) which is the lensmaker’s formula.

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