{"id":182,"date":"2022-04-28T08:36:14","date_gmt":"2022-04-28T12:36:14","guid":{"rendered":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/?post_type=chapter&p=182"},"modified":"2022-05-12T17:56:39","modified_gmt":"2022-05-12T21:56:39","slug":"11-where-photons-came-from","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/chapter\/11-where-photons-came-from\/","title":{"raw":"WHERE PHOTONS CAME FROM","rendered":"WHERE PHOTONS CAME FROM"},"content":{"raw":"

p. 30<\/p>\r\nA stack of appropriately shaped prisms can stop rays of photons from continuing to radiate:\r\n

\"image\"<\/p>\r\n \r\n\r\n \r\n

p. 31<\/p>\r\nOne could add more prisms with \u201cin-between\u201d front angles to catch more rays radiating from the candle. However, there is a simpler solution. It turns out that a continuous curved surface can do the same thing.\r\n

\"image\"<\/p>\r\nLenses<\/em><\/strong> like this enable projecting rays of photons radiating from a source to a distant location without the loss of intensity with distance squared. The process of producing parallel rays of photons so they form a beam<\/em> is called collimation.<\/em>\r\n\r\n \r\n

p. 32<\/p>\r\nAny given lens curvature only bends the rays a certain amount depending on its refractive index. The above lens only collimated the rays from a candle at a certain distance.\r\n\r\nRays from a closer candle enter the lens at angles too steep be bent parallel. They still spread out, though less. Those rays from a further candle that reach the lens, diverge less. Being diffracted the same amount as rays from the other candles, they get bent too much and converge:\r\n

\"image\"<\/p>\r\nThe source distance at which a lens produces collimated rays is the lens\u2019 focal<\/em><\/strong> length<\/em><\/strong>.\r\n\r\n \r\n

p.33<\/p>\r\nNow consider the reverse of the above figure. (Physicists are fond of proclaiming that their laws are the same regardless of the direction of time.) But rather than think backwards, let\u2019s reverse the above figures. Now rays from a candle far out of sight to the left are collimated when they arrive.\r\n

A<\/strong> distance<\/strong> over<\/strong> 3<\/strong> meters<\/strong> is<\/strong> far<\/em><\/strong> enough<\/strong> for<\/strong> most<\/strong> optical<\/strong> applications<\/strong>.<\/p>\r\nTherefore the rays from that candle will converge to a point a focal<\/em><\/strong> length<\/em><\/strong> behind the lens. At that distance there is an image<\/em><\/strong> of that candle:\r\n\r\n\"\"\r\n\r\nBut the image is upside down ?\r\n\r\nThough off page, the real candle is<\/strong> right side up.\r\n\r\nTo see why the image is inverted, follow the rays on the next page:\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

p. 34<\/p>\r\nBy bending the rays even more, it is possible to bring them all back together for an image of a source that is closer than infinity. <\/em>This could be done with steeper rounding of the front surface of the above lens.\u00a0 However, recall that light also gets bent when it speeds up as it leaves a denser medium. Also recall that Lambert\u2019s Law operates in reverse too - rays striking a surface at a steeper angle enter less effectively.\u00a0 Therefore a more elegant solution is to curve both sides of the above lens:\r\n\r\n\"\"\r\n\r\nSimple geometry determines that lenses<\/em><\/strong> invert (and also reverse) the resulting image<\/em><\/strong>\r\n\r\n \r\n

p. 35<\/p>\r\nTwo geometric principles govern how simple lenses transmit rays:\r\n

    \r\n \t
  1. \r\n
      \r\n \t
    1. Rays passing through the lens\u2019 center continue in the same direction.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n2a. Rays passing through the lens\u2019 focal point emerge perpendicular to the lens.\r\n

      or - since rays work the same in reverse<\/p>\r\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2b. Rays perpendicular the lens pass through its focal point after emerging.\r\n

      \"image\"<\/p>\r\n

      Distance<\/strong> and<\/strong> size<\/strong> of<\/strong> an<\/strong> image<\/strong> depend<\/strong> only<\/strong> on<\/strong> source<\/strong> distance<\/strong> and<\/strong> the<\/strong> lens\u2019<\/strong> focal<\/strong> length<\/strong> -<\/strong> ideally.<\/strong><\/p>\r\n \r\n

      p. 36<\/p>\r\nNow For That Page 15 Question About Brightness And Distance:\r\n

      Since<\/em> light<\/em> intensity<\/em> decreases<\/em> with<\/em> the<\/em> square<\/em> of<\/em> distance<\/em> from<\/em> a<\/em> source,<\/em> why<\/em> don\u2019t<\/em> lamps<\/em> get<\/em> dimmer<\/em> as<\/em> you<\/em> back<\/em> away<\/em> from<\/em> them?<\/em><\/p>\r\n

      \"image\"<\/p>\r\nOnly 1\/4 as many photons reach the eye at 2 meters. However, the image extends over only 1\/4 as much area. Therefore the image is just as bright.\r\n\r\nThe same occurs at any distance for any thing that emits or reflects photons.","rendered":"

      p. 30<\/p>\n

      A stack of appropriately shaped prisms can stop rays of photons from continuing to radiate:<\/p>\n

      \"image\"<\/p>\n

       <\/p>\n

       <\/p>\n

      p. 31<\/p>\n

      One could add more prisms with \u201cin-between\u201d front angles to catch more rays radiating from the candle. However, there is a simpler solution. It turns out that a continuous curved surface can do the same thing.<\/p>\n

      \"image\"<\/p>\n

      Lenses<\/em><\/strong> like this enable projecting rays of photons radiating from a source to a distant location without the loss of intensity with distance squared. The process of producing parallel rays of photons so they form a beam<\/em> is called collimation.<\/em><\/p>\n

       <\/p>\n

      p. 32<\/p>\n

      Any given lens curvature only bends the rays a certain amount depending on its refractive index. The above lens only collimated the rays from a candle at a certain distance.<\/p>\n

      Rays from a closer candle enter the lens at angles too steep be bent parallel. They still spread out, though less. Those rays from a further candle that reach the lens, diverge less. Being diffracted the same amount as rays from the other candles, they get bent too much and converge:<\/p>\n

      \"image\"<\/p>\n

      The source distance at which a lens produces collimated rays is the lens\u2019 focal<\/em><\/strong> length<\/em><\/strong>.<\/p>\n

       <\/p>\n

      p.33<\/p>\n

      Now consider the reverse of the above figure. (Physicists are fond of proclaiming that their laws are the same regardless of the direction of time.) But rather than think backwards, let\u2019s reverse the above figures. Now rays from a candle far out of sight to the left are collimated when they arrive.<\/p>\n

      A<\/strong> distance<\/strong> over<\/strong> 3<\/strong> meters<\/strong> is<\/strong> far<\/em><\/strong> enough<\/strong> for<\/strong> most<\/strong> optical<\/strong> applications<\/strong>.<\/p>\n

      Therefore the rays from that candle will converge to a point a focal<\/em><\/strong> length<\/em><\/strong> behind the lens. At that distance there is an image<\/em><\/strong> of that candle:<\/p>\n

      \"\"<\/p>\n

      But the image is upside down ?<\/p>\n

      Though off page, the real candle is<\/strong> right side up.<\/p>\n

      To see why the image is inverted, follow the rays on the next page:<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      p. 34<\/p>\n

      By bending the rays even more, it is possible to bring them all back together for an image of a source that is closer than infinity. <\/em>This could be done with steeper rounding of the front surface of the above lens.\u00a0 However, recall that light also gets bent when it speeds up as it leaves a denser medium. Also recall that Lambert\u2019s Law operates in reverse too – rays striking a surface at a steeper angle enter less effectively.\u00a0 Therefore a more elegant solution is to curve both sides of the above lens:<\/p>\n

      \"\"<\/p>\n

      Simple geometry determines that lenses<\/em><\/strong> invert (and also reverse) the resulting image<\/em><\/strong><\/p>\n

       <\/p>\n

      p. 35<\/p>\n

      Two geometric principles govern how simple lenses transmit rays:<\/p>\n

        \n
      1. \n
          \n
        1. Rays passing through the lens\u2019 center continue in the same direction.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

          2a. Rays passing through the lens\u2019 focal point emerge perpendicular to the lens.<\/p>\n

          or – since rays work the same in reverse<\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2b. Rays perpendicular the lens pass through its focal point after emerging.<\/p>\n

          \"image\"<\/p>\n

          Distance<\/strong> and<\/strong> size<\/strong> of<\/strong> an<\/strong> image<\/strong> depend<\/strong> only<\/strong> on<\/strong> source<\/strong> distance<\/strong> and<\/strong> the<\/strong> lens\u2019<\/strong> focal<\/strong> length<\/strong> –<\/strong> ideally.<\/strong><\/p>\n

           <\/p>\n

          p. 36<\/p>\n

          Now For That Page 15 Question About Brightness And Distance:<\/p>\n

          Since<\/em> light<\/em> intensity<\/em> decreases<\/em> with<\/em> the<\/em> square<\/em> of<\/em> distance<\/em> from<\/em> a<\/em> source,<\/em> why<\/em> don\u2019t<\/em> lamps<\/em> get<\/em> dimmer<\/em> as<\/em> you<\/em> back<\/em> away<\/em> from<\/em> them?<\/em><\/p>\n

          \"image\"<\/p>\n

          Only 1\/4 as many photons reach the eye at 2 meters. However, the image extends over only 1\/4 as much area. Therefore the image is just as bright.<\/p>\n

          The same occurs at any distance for any thing that emits or reflects photons.<\/p>\n","protected":false},"author":28,"menu_order":11,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-182","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/chapters\/182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/wp\/v2\/users\/28"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/chapters\/182\/revisions"}],"predecessor-version":[{"id":373,"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/chapters\/182\/revisions\/373"}],"part":[{"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/chapters\/182\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/wp\/v2\/media?parent=182"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/pressbooks\/v2\/chapter-type?post=182"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/wp\/v2\/contributor?post=182"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.library.upei.ca\/danceofphotons\/wp-json\/wp\/v2\/license?post=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}