{"id":10865,"date":"2020-12-18T12:02:14","date_gmt":"2020-12-18T06:32:14","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=10865"},"modified":"2020-12-18T15:24:15","modified_gmt":"2020-12-18T09:54:15","slug":"apparent-depth-real-depth-related-refractive-index","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/apparent-depth-real-depth-related-refractive-index\/","title":{"rendered":"How is apparent depth and real depth related to refractive index?"},"content":{"rendered":"<h2><strong>How is apparent depth and real depth related to refractive index?<\/strong><\/h2>\n<ol>\n<li>Figure shows two opaque cups, A and B. Cup A is partially filled with water and cup B is totally filled with water. A similar coin is placed at the bottom of each cup.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97802 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-1.png\" alt=\"apparent depth and real depth 1\" width=\"345\" height=\"144\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-1.png 345w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-1-300x125.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/li>\n<li>When observing from the same position, the coin in cup A cannot be seen, but the coin in cup B can be seen.<\/li>\n<li>With more water in the cup, the image of the coin in cup B is actually at a higher position than that in cup A. This made the coin, which cannot be seen in cup A, visible in cup B without adjusting the position of the eye.<\/li>\n<li>This shows that the position of an image depends on the depth of the water.<\/li>\n<li>Figure shows how a coin in the water is seen by an observer. This effect is caused by the refraction at the surface of the water.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97805 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-5.png\" alt=\"apparent depth and real depth 5\" width=\"240\" height=\"280\" \/><\/li>\n<li>Rays of light coming from the coin are bent away from the normal as they leave the water.<\/li>\n<li>When they reach the eye, they appear to come from a virtual coin, which is above the real coin.<\/li>\n<li>The <strong>apparent depth<\/strong> is the <strong>distance of the virtual image, I from the surface of the water<\/strong>.<\/li>\n<li>The <strong>real depth<\/strong> is the <strong>distance of the real object, O from the surface of the water<\/strong>.<\/li>\n<li>The relation of refractive index, n to real depth and apparent depth is given by:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97807 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-6.png\" alt=\"apparent depth and real depth 6\" width=\"183\" height=\"74\" \/><\/li>\n<\/ol>\n<p><strong>People also ask<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/cbselibrary.com\/refraction-of-light\/\">What is Refraction of Light?<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/natural-phenomenon-due-refraction-light\/\">Examples of refraction of light<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/measure-refractive-index\/\">What is the index of refraction?<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/atmospheric-refraction\/\">What is atmospheric refraction?<\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/refraction-of-light-through-glass-slab\/\">Refraction of light through\u00a0glass slab<\/a><\/li>\n<\/ul>\n<h2><strong>Real and Apparent Depth Experiment<\/strong><\/h2>\n<p><strong>Aim:<\/strong> To find the relationship between the real depth and the apparent depth of an object placed in water.<br \/>\n<strong>Problem:<\/strong> How does the apparent depth of an object in water vary with its real depth?<br \/>\n<strong>Hypothesis:<\/strong> When the real depth of an object in water increases, its apparent depth also increases. Variables:<br \/>\n(a) Manipulated variable: Real depth,\u00a0d<sub>1<\/sub><br \/>\n(b) Responding variable: Apparent depth,\u00a0d<sub>2<\/sub><br \/>\n(c) Fixed variable: The density of water<br \/>\n<strong>Materials:<\/strong> 2 steel pins, 1 cork, jug of water<br \/>\n<strong>Apparatus:<\/strong> Tall beaker, metre rule, retort stand<br \/>\n<strong>Method:<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-97809 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-2.png\" alt=\"apparent depth and real depth 2\" width=\"296\" height=\"283\" \/><\/p>\n<ol>\n<li>The apparatus is set up as shown in Figure.<\/li>\n<li>A steel pin (Pin O) is placed at the bottom of the tall beaker.<\/li>\n<li>The other steel pin is fixed on a cork that is held by the clamp of a retort stand. It is used as a search pin (Pin l).<\/li>\n<li>The tall beaker is filled with water to a height of d<sub>1<\/sub>\u00a0= 20 cm (the real depth).<\/li>\n<li>The image of the steel pin is viewed vertically above the edge of the beaker.<\/li>\n<li>The search pin which is adjacent to the beaker is then moved up or down until it is levelled with the image of the steel pin seen through the water.<\/li>\n<li>The position of the image, d<sub>2<\/sub>\u00a0(the apparent depth) is measured using the metre rule.<\/li>\n<li>Steps 4 to 7 are repeated with d<sub>1<\/sub>\u00a0= 30 cm, 40 cm, 50 cm and 60 cm. The results are recorded in Table.<\/li>\n<li>A graph of real depth (d<sub>1<\/sub>) against apparent depth (d<sub>2<\/sub>) is plotted.<\/li>\n<\/ol>\n<p><strong>Results:<\/strong><br \/>\n1. Tabulation of results.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-97812 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-3.png\" alt=\"apparent depth and real depth 3\" width=\"432\" height=\"167\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-3.png 432w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-3-300x116.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/p>\n<p>2. Graph of real depth (d<sub>1<\/sub>) against apparent depth (d<sub>2<\/sub>).<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-97814 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-4.png\" alt=\"apparent depth and real depth 4\" width=\"402\" height=\"277\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-4.png 402w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-4-300x207.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p><strong>Discussion:<\/strong><\/p>\n<ol>\n<li>The apparent depth is always smaller than the real depth.<\/li>\n<li>When the real depth increases, the apparent depth also increases.<\/li>\n<li>The graph of real depth d<sub>1<\/sub>\u00a0against the apparent depth d<sub>2<\/sub>\u00a0is a straight line graph passing through the origin. This shows that the apparent depth is directly proportional to the real depth.<\/li>\n<li>The gradient of the graph of real depth d<sub>1<\/sub>\u00a0against apparent depth d<sub>2<\/sub>\u00a0is the refractive index of water.<\/li>\n<\/ol>\n<p><strong>Conclusions:<\/strong><\/p>\n<ol>\n<li>The results of the experiment support the hypothesis.<\/li>\n<li>The ratio of Real depth to Apparent depth is the refractive index of water.<\/li>\n<\/ol>\n<h2><strong>Real and Apparent Depth\u00a0Problems<\/strong><\/h2>\n<ol>\n<li>A fish at the bottom of a pond appears to be 1.2 m from the water surface. What is the depth of the pond?<br \/>\n[Refractive index of water = 1.33]<br \/>\n<strong>Solution:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97847\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-7.png\" alt=\"apparent depth and real depth 7\" width=\"291\" height=\"167\" \/><br \/>\n<\/strong><\/li>\n<li>Figure shows a boy standing inside a swimming pool. His legs appear shorter when his friend observes him from the pool side.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97849\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-8.png\" alt=\"apparent depth and real depth 8\" width=\"268\" height=\"206\" \/><br \/>\n(a) Explain how this phenomenon occurs.<br \/>\n(b) Draw a ray diagram to show how his legs appear shorter.<br \/>\n(c) If the depth of the pool is 0.8 m, calculate the distance of the image of his feet as seen from the surface of the water.<br \/>\n[Refractive index of water = 1.33]<br \/>\n<strong>Solution:<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-97850\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-9.png\" alt=\"apparent depth and real depth 9\" width=\"364\" height=\"497\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-9.png 364w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/03\/apparent-depth-and-real-depth-9-220x300.png 220w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How is apparent depth and real depth related to refractive index? Figure shows two opaque cups, A and B. Cup A is partially filled with water and cup B is totally filled with water. A similar coin is placed at the bottom of each cup. When observing from the same position, the coin in cup &#8230; <a title=\"How is apparent depth and real depth related to refractive index?\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/apparent-depth-real-depth-related-refractive-index\/\" aria-label=\"More on How is apparent depth and real depth related to refractive index?\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[404],"tags":[3925,3934,3923,3929,3932,3928,3924,3926,3933,3931,3930,3927],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How is apparent depth and real depth related to refractive index? - CBSE Library<\/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:\/\/cbselibrary.com\/apparent-depth-real-depth-related-refractive-index\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How is apparent depth and real depth related to refractive index?\" \/>\n<meta property=\"og:description\" content=\"How is apparent depth and real depth related to refractive index? 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Figure shows two opaque cups, A and B. Cup A is partially filled with water and cup B is totally filled with water. A similar coin is placed at the bottom of each cup. When observing from the same position, the coin in cup ... 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