The Thin Lens Equation. These lenses have negligible thickness. 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. This one is easy to remember: hi over ho equals i over o! Consider the thick bi-convex lens shown in Figure \(\PageIndex{8}\). The triangles KGC and DHC are also similar, so hi divided by h o is equal to i divided by o. Focal length. Let F be the principle focus and f be the focal length. Figure 3. Our first step is to determine the conditions for which a lens will produce an image, be it real or virtual. Use equations (1) and (2) to derive the thin lens equation 1/f = 1/i + 1/o by yourself. The formula is as follows: \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) Lens Formula Derivation. 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). Consider a convex lens with an optical center O. 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. Take a moment to study the geometry! This is equation (1). To predict exactly what a lens will do, we can use the thin lens equation: (1/do) + (1/di) = 1/f. This is more intuitive to see how lens equation is derived. Lens formula is applicable for convex as well as concave lenses. and so = + + = − + = − + = −. This is equation (2). 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. In this equation, do is the object distance or the distance of the object from the center of the lens. 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