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 \(n_2\). Performance & security by Cloudflare, Please complete the security check to access. Legal. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Cloudflare Ray ID: 5f9aed590889eddb 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. Magnification of a lens is defined as the ratio of the height of an image to the height of an object. Your IP: 62.210.115.126 • View Answer. Establish Lens maker's formula f 1 = (μ − 1) (R 1 1 − R 2 1 ) MEDIUM. 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 \(\PageIndex{1a}\). You may need to download version 2.0 now from the Chrome Web Store. Derivation of Lens formula for thin lenses and magnification formula for lenses by Utpal Sir. To obtain a magnification of − 2, the object has to be moved a distance equal to: MEDIUM. The magnification of an object placed in front of a convex lens of focal length 2 0 c m is + 2. Figure II.14 shows an optical element separating media of indices \(n_1\) and \(n_2\). It is represented by the symbol m. The size of an image formed by a lens varies with the position of the object. 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. The following assumptions are taken for the derivation of lens maker formula. The focal length of a lens depends on : EASY. 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, \[ \text{magnification} = \dfrac{n_1q}{n_2p} = \frac{C_1}{C_2}. It is equal to the ratio of image distance to that of object distance. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Let the refractive indices of the surrounding medium and the lens material be n1 and n2 respectively. \label{eq:2.9.1} \], Jeremy Tatum (University of Victoria, Canada). Magnification when the image is at infinity. In this video I showed the derivation of magnification formula for lenses. m = \frac {h_i} {h_o} = \frac {v} {u} 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. Another way to prevent getting this page in the future is to use Privacy Pass. 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. View Answer. Have questions or comments? It is also given in terms of image distance and object distance. [ "article:topic", "authorname:tatumj", "Magnification", "showtoc:no", "license:ccbync" ]. Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures R1 and R2 respectively. Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm. 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. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Watch the recordings here on Youtube! View Answer. 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). Missed the LibreFest? An image of height \(h'\) is formed at a distance \(q\) of an object of height \(h\) at a distance \(p\). For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Derivation. 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. • Also given in terms of image distance to that of object distance image by... 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