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