{"product_id":"where-is-the-image-exploring-reflection-with-mirrors","title":"Where Is the Image? — Exploring Reflection with Mirrors","description":"\u003ch3 class=\"PDq2pG_selectionAnchorContainer\"\u003eThere is an image behind a mirror.\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h3\u003e\n\u003ch3\u003eBut there is nothing actually there.\u003c\/h3\u003e\n\u003ch3\u003eCan you find its position?\u003c\/h3\u003e\n\u003ch3\u003eAnd what happens when light is allowed to reflect more than once?\u003c\/h3\u003e\n\u003ch3\u003eWith two simple investigations, we can discover both the location of a virtual image and the surprising appearance of multiple images from a single object.\u003c\/h3\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003ePart 1 — Finding the Image Behind a Mirror\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eA plane mirror was placed vertically on a table.\u003c\/p\u003e\n\u003cp\u003eA large pencil was placed in front of it.\u003c\/p\u003e\n\u003cp\u003eBecause the pencil was larger than the mirror, only part of it could be seen in the reflected image.\u003c\/p\u003e\n\u003cp\u003eA second, identical pencil was then placed behind the mirror.\u003c\/p\u003e\n\u003cp\u003eThe goal was simple:\u003c\/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003e\u003cstrong\u003eCan you position the second pencil exactly where the image of the first pencil appears to be?\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/blockquote\u003e\n\u003cp\u003eAt first, the two pencils appeared to align.\u003c\/p\u003e\n\u003cp\u003eBut when the observer moved sideways, the alignment disappeared.\u003c\/p\u003e\n\u003cp\u003eThe second pencil was adjusted repeatedly.\u003c\/p\u003e\n\u003cp\u003eEventually, a position was found where:\u003c\/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003e\u003cstrong\u003eThe real pencil and the reflected image appeared to coincide from every viewing position.\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/blockquote\u003e\n\u003cp\u003eThe position of the second pencil marked the apparent position of the virtual image.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eThe Remarkable Result\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThe distance from the real pencil to the mirror was measured.\u003c\/p\u003e\n\u003cp\u003eThen the distance from the mirror to the second pencil was measured.\u003c\/p\u003e\n\u003cp\u003eThey were equal.\u003c\/p\u003e\n\u003cp\u003e\u003cspan role=\"math\"\u003e\u003cspan class=\"katex-display\"\u003e\u003cspan class=\"katex\"\u003e\u003cspan class=\"katex-html\"\u003e\u003cspan class=\"base\"\u003e\u003cspan class=\"strut\"\u003e\u003c\/span\u003e\u003cspan class=\"mord\"\u003e\u003cspan class=\"vlist-t vlist-t2\"\u003e\u003cspan class=\"vlist-r\"\u003e\u003cspan class=\"vlist\"\u003e\u003cspan\u003e\u003cspan class=\"pstrut\"\u003e\u003c\/span\u003e\u003cspan class=\"boxpad\"\u003e\u003cspan class=\"mord text\"\u003eObject distance\u003c\/span\u003e\u003cspan class=\"mspace\"\u003e\u003c\/span\u003e\u003cspan class=\"mrel\"\u003e=\u003c\/span\u003e\u003cspan class=\"mspace\"\u003e\u003c\/span\u003e\u003cspan class=\"mord text\"\u003eImage distance\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003cspan\u003e\u003cspan class=\"pstrut\"\u003e\u003c\/span\u003e\u003cspan class=\"stretchy fbox\"\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003cspan class=\"vlist-s\"\u003e\u003c\/span\u003e\u003c\/span\u003e\u003cspan class=\"vlist-r\"\u003e\u003cspan class=\"vlist\"\u003e\u003cspan\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003eThis is one of the fundamental properties of a plane mirror.\u003c\/p\u003e\n\u003cp\u003eThe image appears to be located exactly as far behind the mirror as the object is in front of it.\u003c\/p\u003e\n\u003cp\u003eBut there is no physical object at that location.\u003c\/p\u003e\n\u003cp\u003eThe image is \u003cstrong\u003evirtual\u003c\/strong\u003e.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eWhy Does It Work?\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThis is a perfect point to ask visitors to investigate using geometrical optics.\u003c\/p\u003e\n\u003cp\u003eChoose a point on the pencil.\u003c\/p\u003e\n\u003cp\u003eDraw rays travelling from that point toward the mirror.\u003c\/p\u003e\n\u003cp\u003eReflect those rays according to the law of reflection.\u003c\/p\u003e\n\u003cp\u003eNow extend the reflected rays backward.\u003c\/p\u003e\n\u003cp\u003eThey appear to originate from a point behind the mirror.\u003c\/p\u003e\n\u003cp\u003eRepeat this for different points on the pencil.\u003c\/p\u003e\n\u003cp\u003eThe complete virtual image emerges.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eA Better Experimental Test\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThe sideways movement of the observer is actually an important part of your experiment.\u003c\/p\u003e\n\u003cp\u003eIf the second pencil is not exactly at the image position, \u003cstrong\u003eparallax\u003c\/strong\u003e appears.\u003c\/p\u003e\n\u003cp\u003eMove your head from left to right.\u003c\/p\u003e\n\u003cp\u003eIf the image and the second pencil move relative to each other, their depths are different.\u003c\/p\u003e\n\u003cp\u003eWhen there is no relative motion, the two are at the same apparent depth.\u003c\/p\u003e\n\u003cp\u003eThis is essentially a simple optical method for determining the position of an invisible object.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003ePart 2 — One Object, Many Images\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThe second investigation reveals another surprising property of mirrors.\u003c\/p\u003e\n\u003cp\u003eA thick glass mirror was placed in front of a bright object.\u003c\/p\u003e\n\u003cp\u003eA light stick was used first.\u003c\/p\u003e\n\u003cp\u003eWhen viewed approximately perpendicular to the mirror, only the expected image was obvious.\u003c\/p\u003e\n\u003cp\u003eBut as the viewing angle became larger, additional images appeared.\u003c\/p\u003e\n\u003cp\u003eThe effect became even clearer in a dark room with a candle.\u003c\/p\u003e\n\u003cp\u003eInstead of seeing a single image, multiple images could be distinguished.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eWhy Multiple Images?\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eA thick mirror is not optically just a single reflecting surface.\u003c\/p\u003e\n\u003cp\u003eIt contains several interfaces.\u003c\/p\u003e\n\u003cp\u003eFor example:\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eair → glass → reflective coating → glass → air\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003eLight can undergo reflections at more than one of these surfaces.\u003c\/p\u003e\n\u003cp\u003eSome of these reflections produce images that are extremely weak.\u003c\/p\u003e\n\u003cp\u003eUnder ordinary viewing conditions, they are difficult to notice.\u003c\/p\u003e\n\u003cp\u003eBut at larger viewing angles, the geometry and relative brightness of these reflected images change, making the additional images easier to see.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eWhy Use a Candle or Bright Light?\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThis is an important question for visitors.\u003c\/p\u003e\n\u003cp\u003eThe additional reflections are much weaker than the main reflection.\u003c\/p\u003e\n\u003cp\u003eA bright source produces enough light for these faint images to become visible.\u003c\/p\u003e\n\u003cp\u003eA dark room helps further because there is less competing background light.\u003c\/p\u003e\n\u003cp\u003eThis is why the candle experiment is much more revealing than trying the same thing with a dim object.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eThe Interesting Question\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThe experiment leaves several things to investigate:\u003c\/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003e\u003cstrong\u003eWhy do additional images become visible only at larger viewing angles?\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/blockquote\u003e\n\u003cp\u003eAnd:\u003c\/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003e\u003cstrong\u003eWhy does a thick mirror produce more than one image?\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/blockquote\u003e\n\u003cp\u003eVisitors can investigate:\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe different glass surfaces.\u003c\/li\u003e\n\u003cli\u003eThe reflective coating.\u003c\/li\u003e\n\u003cli\u003eFresnel reflection.\u003c\/li\u003e\n\u003cli\u003eAngle of incidence.\u003c\/li\u003e\n\u003cli\u003eRelative brightness of the images.\u003c\/li\u003e\n\u003cli\u003eSeparation between the multiple images.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003eThis is a beautiful example of a phenomenon that is normally hidden by the design of everyday objects.\u003c\/p\u003e\n\u003ch1 class=\"PDq2pG_selectionAnchorContainer\"\u003eThe Deeper Connection\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h1\u003e\n\u003cp\u003eThere are actually \u003cstrong\u003etwo different scientific ideas\u003c\/strong\u003e hiding in this experiment.\u003c\/p\u003e\n\u003ch3\u003eFirst:\u003c\/h3\u003e\n\u003cp\u003eWe can determine the location of something we cannot physically touch.\u003c\/p\u003e\n\u003cp\u003eThe virtual image is invisible as an object, yet its position can be experimentally measured.\u003c\/p\u003e\n\u003ch3\u003eSecond:\u003c\/h3\u003e\n\u003cp\u003eA seemingly simple optical component can contain several optical paths.\u003c\/p\u003e\n\u003cp\u003eThe thick mirror is producing information that is normally hidden because one reflection is overwhelmingly brighter than the others.\u003c\/p\u003e\n\u003cp\u003eBoth are good examples of an important experimental principle:\u003c\/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003e\u003cstrong\u003eCareful observation can reveal effects that ordinary observation hides.\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/blockquote\u003e\n\u003ch3 class=\"PDq2pG_selectionAnchorContainer\"\u003eContinue the Investigation\u003cspan class=\"PDq2pG_selectionAnchor\"\u003e\u003c\/span\u003e\n\u003c\/h3\u003e\n\u003cp\u003eThe experiment you've just explored is only the beginning. Our hands-on investigation sets are designed to help you recreate, extend, and deepen these ideas through observation and experimentation.\u003c\/p\u003e\n\u003cp\u003eEvery investigation has the potential to lead to a new question. If you discover something interesting, improve the experiment, or develop a new variation, share it with the Geometers community. Your work may inspire others and could even be featured here.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eKeep experimenting. Keep questioning. Keep discovering.\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003ciframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/FjpJl9RsFe8?si=BNomtCmZ4g5eHEvw\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen\u003e\u003c\/iframe\u003e","brand":"Geometers","offers":[{"title":"Default Title","offer_id":46362389479560,"sku":null,"price":499.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0725\/3891\/4952\/files\/1.png?v=1786529202","url":"https:\/\/geometers.in\/products\/where-is-the-image-exploring-reflection-with-mirrors","provider":"Geometers","version":"1.0","type":"link"}