{"id":1712,"date":"2023-03-16T09:00:57","date_gmt":"2023-03-16T03:30:57","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=1712"},"modified":"2023-03-16T10:00:34","modified_gmt":"2023-03-16T04:30:34","slug":"numerical-methods-in-lens","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/numerical-methods-in-lens\/","title":{"rendered":"Lens Formula &#038; Magnification \u2013 Lens Power"},"content":{"rendered":"<h2><strong>Numerical Methods In Lens<\/strong><\/h2>\n<p><strong>(A)\u00a0<\/strong><strong>Lens Formula \u00a0 <\/strong><\/p>\n<ul>\n<li><strong>Definition:<\/strong> The equation relating the object distance (u), the image distance (v) and the focal length (f) of the lens is called the lens formula.<br \/>\n<strong>Assumptions made:<\/strong><\/p>\n<ol>\n<li>The lens is <strong>thin.<\/strong><\/li>\n<li>The lens has a <strong>small aperture<\/strong>.<\/li>\n<li>\u00a0The object lies <strong>close<\/strong> to principal axis.<\/li>\n<li>The incident rays make <strong>small angles<\/strong> with the lens surface or the principal axis.<\/li>\n<\/ol>\n<\/li>\n<li>When a lens of known focal length, f is used to find the relationship between the object distance,<br \/>\nu and the image distance v, the value of (1\/u + 1\/v) is a constant.<\/li>\n<li>This constant value is equal to 1\/f.<br \/>\nTherefore, the relationship between the object distance, the image distance and the focal length of a lens is given by the<br \/>\n\\( \\text{Lens Formula:\u00a0\u00a0 }\\frac{1}{u}+\\frac{1}{v}=\\frac{1}{f} \\)<\/li>\n<li>The lens formula may be applied to convex lenses as well as concave lenses provided the \u2018real is positive\u2019 sign convention is followed.<\/li>\n<li>Table shows the sign convention for the values of object distance, image distance and focal length. All distances are measured from the optical centre of the lens.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97277\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula.png\" alt=\"Lens Formula\" width=\"373\" height=\"210\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula.png 373w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-300x169.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/li>\n<\/ul>\n<p><strong>People also ask<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.aplustopper.com\/what-is-a-lens\/\">What is a Lens?<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/types-of-spherical-lenses\/\">What are the Types of Spherical Lenses<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/image-formation-by-concave-convex-lenses\/\">Image Formation By Concave And Convex Lenses<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/uses-of-lenses-in-optical-devices\/\">The Uses of Lenses in Optical Devices<\/a><\/li>\n<li><a href=\"https:\/\/www.aplustopper.com\/construct-optical-devices-using-lenses\/\">To Construct Optical Devices Using Lenses<\/a><\/li>\n<\/ul>\n<p><strong>(B) Linear Magnification For Lens<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-97347 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens.png\" alt=\"Linear Magnification Lens\" width=\"376\" height=\"181\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens.png 376w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-300x144.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p><strong>Definition:<\/strong> 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. It is represented by the symbol m.<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>The size of an image formed by a lens varies with the position of the object.<\/li>\n<li>The simplest way to compare the image with the object is by the ratio of their sizes. This ratio is the<strong> linear magnification<\/strong>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97408 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-1.png\" alt=\"Linear Magnification Lens 1\" width=\"349\" height=\"55\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-1.png 349w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-1-300x47.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li>The ratio of the image size to the object size is the same as the ratio of the image distance to the object distance.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97358 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-2.png\" alt=\"Linear Magnification Lens 2\" width=\"342\" height=\"91\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-2.png 342w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-2-300x80.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/li>\n<li>In symbols,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97361 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Linear-Magnification-Lens-3.png\" alt=\"Linear Magnification Lens 3\" width=\"202\" height=\"75\" \/><\/li>\n<\/ul>\n<p><strong>(C) Power Of Lens<\/strong><\/p>\n<p><strong>Definition:<\/strong> It is the capacity or the ability of a lens to deviate (converge or diverge) the path of rays passing through it.<\/p>\n<ul>\n<li>A lens producing more converging or more diverging, is said to have more power.<\/li>\n<li>The power of a lens is related to its focal length, f by the equation:<br \/>\n\\( \\text{Power of lens }\\left( \\text{in diopter} \\right)\\propto \\frac{1}{\\text{f (in}\\,\\,\\text{metre)}}\\)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97365\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/lens-power.png\" alt=\"lens power\" width=\"324\" height=\"155\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/lens-power.png 324w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/lens-power-300x144.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/li>\n<li>The unit for power is dioptre (D).<\/li>\n<li>The shorter the focal length, the greater the power.<\/li>\n<li>The power for a convex lens is positive and the power for a concave lens is negative.<\/li>\n<\/ul>\n<h2><strong>Lens Equation Problems and Solutions<\/strong><\/h2>\n<ol>\n<li>Figure shows a graph of v against u.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97367\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems.png\" alt=\"Lens Formula Problems\" width=\"239\" height=\"300\" \/><br \/>\nDetermine the focal length of the lens.<br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97369\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-1.png\" alt=\"Lens Formula Problems 1\" width=\"285\" height=\"297\" \/><br \/>\nFrom the graph, when v = u, the coordinate of the point of intersection is given as (2f, 2f), where f is the focal length of the lens.<br \/>\n2f = 30<br \/>\nf = 15 cm<br \/>\nThe focal length of the lens is 15 cm.<\/li>\n<li>Figure shows a graph of v against magnification, m for a lens experiment.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97370\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-2.png\" alt=\"Lens Formula Problems 2\" width=\"374\" height=\"262\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-2.png 374w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-2-300x210.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nWhat is the focal length of the lens used in the experiment?<br \/>\n<strong>Solution:<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97377\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-3.png\" alt=\"Lens Formula Problems 3\" width=\"286\" height=\"172\" \/><br \/>\nThis is the general equation for the straight line in a graph of v against m. From the graph, the focal length of the lens is 15 cm (Gradient of graph or intercept at v-axis).<\/li>\n<li>An object is placed in front of a convex lens with a focal length, f of 10 cm. What are the characteristics of the image formed if the object distance is 15 cm?<br \/>\n<strong>Solution:<\/strong><br \/>\nObject distance, u = +15 cm (real object);<br \/>\nFocal length, f = +10 cm (convex lens);<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97379\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-4.png\" alt=\"Lens Formula Problems 4\" width=\"253\" height=\"332\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-4.png 253w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-4-229x300.png 229w\" sizes=\"(max-width: 253px) 100vw, 253px\" \/><br \/>\nTherefore, the image is real, inverted, 30 cm from the lens, on the opposite side of the object and magnified 2 times.<\/li>\n<li>An object of height 6 cm is placed at a distance of 20 cm from a concave lens. Its focal length is 10 cm. Find the position and size of the image.<br \/>\n<strong>Solution:<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97381\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-5.png\" alt=\"Lens Formula Problems 5\" width=\"321\" height=\"453\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-5.png 321w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-5-213x300.png 213w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nThe image is virtual, at a distance of 6.7 cm from the lens on the same side as the object and has a height of 2 cm.<\/li>\n<li>Figure shows the position of an image, I of an object, O formed by a convex lens. The height of the object, ho is 5 cm.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97384\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-6.png\" alt=\"Lens Formula Problems 6\" width=\"383\" height=\"120\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-6.png 383w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-6-300x94.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\nWhat is the height of the image, h<sub>o<\/sub>\u00a0?<br \/>\n<strong>Solution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97386\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Lens-Formula-Problems-7.png\" alt=\"Lens Formula Problems 7\" width=\"290\" height=\"222\" \/><br \/>\n<\/strong><\/li>\n<\/ol>\n<h2><strong>Focal Length of Convex Lens Experiment<\/strong><\/h2>\n<p><strong>Aim:<\/strong> To find the relationship between the object distance, u, image distance, v and the focal length, f of a lens.<br \/>\n<strong>Apparatus:<\/strong> Light bulb, convex lens (f = 15 cm), metre rule, white screen, lens holder<br \/>\n<strong>Method:<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97394\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment.png\" alt=\"Focal Length of Convex Lens Experiment\" width=\"624\" height=\"275\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment.png 624w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-300x132.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><\/p>\n<ol>\n<li>The apparatus is set up as shown in figure.<\/li>\n<li>The light bulb is kept at a fixed position at one end of the metre rule. The convex lens is moved to a position where the object distance, u = 40 cm. The bulb is switched on and the screen is moved backward and forward to get a sharp image formed on it. The image distance, v is measured and recorded.<\/li>\n<li>Step 2 is repeated for object distances, u = 35 cm, 30 cm, 25 cm, 20 cm and 18 cm. All the corresponding values of the image distance, v are measured and recorded. The results are tabulated in Table.<\/li>\n<li>The values of 1\/u, 1\/v and (1\/u + 1\/v) are calculated and corrected to two significant figures. The mean value for (1\/u + 1\/v) is determined.<\/li>\n<li>The focal length, f of the convex lens used in the activity is given as 15 cm. The value of 1\/f is determined<br \/>\n11 &#8216; and this value is compared with the mean value of (1\/u + 1\/v).<\/li>\n<\/ol>\n<p><strong>Results:<\/strong><\/p>\n<ol>\n<li>The focal length of the lens used, f = 15 cm.<\/li>\n<li>Tabulation of results.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97396\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-1.png\" alt=\"Focal Length of Convex Lens Experiment 1\" width=\"652\" height=\"254\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-1.png 652w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-1-300x117.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><\/li>\n<li>The mean value for (1\/u + 1\/v) is 0.067.<br \/>\nThe focal length, f = 15 cm, the reciprocal, = 1\/f = 0.067 cm<sup>-1<\/sup><\/li>\n<\/ol>\n<p><strong>Discussion:<\/strong><\/p>\n<ol>\n<li>If a graph of 1\/v against 1\/u is plotted, the graph is as shown in Figure.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97401\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-2.png\" alt=\"Focal Length of Convex Lens Experiment 2\" width=\"343\" height=\"301\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-2.png 343w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-2-300x263.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/li>\n<li>The graph is a straight line graph cutting the two axes at two intercepts. The values of the intercepts are both equal to 0.067.<\/li>\n<li>From the graph,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97402\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-3.png\" alt=\"Focal Length of Convex Lens Experiment 3\" width=\"406\" height=\"100\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-3.png 406w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-3-300x74.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/li>\n<\/ol>\n<p><strong>Conclusion:<br \/>\n<\/strong>The relationship between the object distance, u, image distance, v and focal length, f of a lens is<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-97404 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2019\/04\/Focal-Length-of-Convex-Lens-Experiment-4.png\" alt=\"Focal Length of Convex Lens Experiment 4\" width=\"142\" height=\"68\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Numerical Methods In Lens (A)\u00a0Lens Formula \u00a0 Definition: The equation relating the object distance (u), the image distance (v) and the focal length (f) of the lens is called the lens formula. Assumptions made: The lens is thin. The lens has a small aperture. \u00a0The object lies close to principal axis. The incident rays make [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[404],"tags":[593,3957,3956,592,590,591],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Lens Formula &amp; Magnification \u2013 Lens Power - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/numerical-methods-in-lens\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lens Formula &amp; Magnification \u2013 Lens Power\" \/>\n<meta property=\"og:description\" content=\"Numerical Methods In Lens (A)\u00a0Lens Formula \u00a0 Definition: The equation relating the object distance (u), the image distance (v) and the focal length (f) of the lens is called the lens formula. Assumptions made: The lens is thin. The lens has a small aperture. \u00a0The object lies close to principal axis. 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