The triangles KGC and DHC are also similar, so hi divided by h o is equal to i divided by o. The Thin Lens Equation. To predict exactly what a lens will do, we can use the thin lens equation: (1/do) + (1/di) = 1/f. Our first step is to determine the conditions for which a lens will produce an image, be it real or virtual. Take a moment to study the geometry! In this equation, do is the object distance or the distance of the object from the center of the lens. The equation derived for a thin lens and relating two conjugated points is: (2) For the thick lens, so is the distance between the object and the first principal plane, and si is the distance between the second principal plane and the image. This is more intuitive to see how lens equation is derived. Only the real part of 1/q is affected: the wavefront curvature 1/R is reduced by the power of the lens 1/f, while the lateral beam size w remains unchanged upon exiting the thin lens. These lenses have negligible thickness. The focal length, f, of a lens in air is given by the lensmaker's equation: = (−) [− + (−)], where n is the index of refraction of the lens material, and R 1 and R 2 are the radii of curvature of the two surfaces. Consider the thick bi-convex lens shown in Figure \(\PageIndex{8}\). For an image to be produced, all rays at the image plane which come from one particular point on the object must pass through one corresponding particular point in the image plane. These equations, called the thin-lens equation and the lens maker’s equation, allow us to quantitatively analyze thin lenses. This is equation (1). This one is easy to remember: hi over ho equals i over o! Focal length. Let F be the principle focus and f be the focal length. Consider a convex lens with an optical center O. Figure 3. The index of refraction of the surrounding medium is n 1 (if the lens is in air, then \(n_1=1.00\)) and that of the lens is \(n_2\). The thin lens equation is simple and explained by geometrical properties of the lens and light rays. The formula is as follows: \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) Lens Formula Derivation. and so = + + = − + = − + = −. Consider a beam traveling through a thin lens with focal length f. The ray transfer matrix is [] = [− /]. Lens formula is applicable for convex as well as concave lenses. This is equation (2). How to Derive the Thin Lens Equation (1/d o)+(1/d i)=(1/f) If your operating system is not capable of viewing this animation, click (thin lens). Use equations (1) and (2) to derive the thin lens equation 1/f = 1/i + 1/o by yourself. Two special such rays are shown in figure 3.

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