1 R 1! 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. Assumptions made: The lens is thin. n m)! The derivation of the Gaussian form proceeds from triangle geometry. For a thin lens, the lens power P is the sum of the surface powers. The thin lens equation is also sometimes expressed in the Newtonian form. Convex Lens. The lens equation tells us everything we need to know about the image of an object that is a known distance from the plane of a thin lens of known focal length. 2. ; The lens has a small aperture. Again, take the convex lens formula, 1/f = (n-1) (1/R1 -1/R2) where n is the refractive index and R1 and R2 are radii of the two faces of the lens. 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. Here, x 1 and x 2 are the distances to the object and image respectively from the focal points. Lens Formula Derivation. 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. ; The incident rays make small angles with the lens surface or the principal axis. The same derivation used for the thin lens equation can be used to show that for a thick lens provide the effective focal length given by is used, and the distances s o and s i are measured from the principle points located at 1 s i + 1 s o = 1 1 f f = (n l! The sign conventions for the given quantities in the lens equation and magnification equations are as follows: f is + if the lens is a double convex lens (converging lens) f is - if the lens is a double concave lens (diverging lens) d i is + if the image is a real image and located on the opposite side of the lens. The object lies close to principal axis. For a biconvex lens, assuming that R1 = R2, and n= 1.5 roughly for glass,then substituting these values in the above formula, we get the value of f as infinity, which is really absurd. While we have derived it for the case of an object that is a distance greater than the focal length, from a converging lens, it works for all the combinations of lens and object distance for which the thin lens approximation is good. For thicker lenses, Gullstrand's equation can be used to get the equivalent power. 1 R 2 + (n l!
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