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Cloudflare Ray ID: 5f9aed590889eddb It is also given in terms of image distance and object distance. • Missed the LibreFest? It is equal to the ratio of image distance to that of object distance. Figure II.14 shows an optical element separating media of indices \(n_1\) and \(n_2\). • Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Definition: The ratio of the size of the image formed by refraction from the lens to the size of the object, is called linear magnification produced by the lens. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Derivation of Lens formula for thin lenses and magnification formula for lenses by Utpal Sir. Another way to prevent getting this page in the future is to use Privacy Pass. Let the refractive indices of the surrounding medium and the lens material be n1 and n2 respectively. To obtain a magnification of − 2, the object has to be moved a distance equal to: MEDIUM. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. We assume that the object is situated at the near point of the eye, because this is the object distance at which the unaided eye can form the largest image on the retina. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Suppose the object has a height h. The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i.e., a distance D. Legal. Derivation. It is represented by the symbol m. The size of an image formed by a lens varies with the position of the object. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. View Answer. 2.9: Derivation of Magnification Last updated; Save as PDF Page ID 8302; Contributed by Jeremy Tatum; Emeritus Professor (Physics & Astronomy) at University of Victoria; Contributor; Figure II.14 shows an optical element separating media of indices \(n_1\) and \(n_2\). Establish Lens maker's formula f 1 = (μ − 1) (R 1 1 − R 2 1 ) MEDIUM. Your IP: 62.210.115.126 The magnification of an object placed in front of a convex lens of focal length 2 0 c m is + 2. You may need to download version 2.0 now from the Chrome Web Store. [ "article:topic", "authorname:tatumj", "Magnification", "showtoc:no", "license:ccbync" ]. m = \frac {h_i} {h_o} = \frac {v} {u} \label{eq:2.9.1} \], Jeremy Tatum (University of Victoria, Canada). The following assumptions are taken for the derivation of lens maker formula. View Answer. Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures R1 and R2 respectively. The focal length of a lens depends on : EASY. I have drawn the element as an interface, though it could equally well be a lens (or, if I were to fold the drawing, a mirror). Magnification when the image is at infinity. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. To account for the magnification of a magnifying lens, we compare the angle subtended by the image (created by the lens) with the angle subtended by the object (viewed with no lens), as shown in Figure \(\PageIndex{1a}\). View Answer. An image of height \(h'\) is formed at a distance \(q\) of an object of height \(h\) at a distance \(p\). Magnification of a lens is defined as the ratio of the height of an image to the height of an object. In this video I showed the derivation of magnification formula for lenses. Assuming, as ever, that angles are small, we have, \[\text{magnification} = \dfrac{\theta_2q}{\theta_1p}.\], But Snell’s law, for small angles, is \(n_1\theta_1 = n_2\theta_2\) , and therefore, \[ \text{magnification} = \dfrac{n_1q}{n_2p} = \frac{C_1}{C_2}. Watch the recordings here on Youtube! Have questions or comments? 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