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348 lines
14 KiB
HTML
348 lines
14 KiB
HTML
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Refraction</h1>
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<p class="center"><img src="images/refraction-fish.jpg" alt="refraction fish" height="153" width="600"></p>
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Refraction is the "bending" of light (or any <a href="electromagnetic-spectrum.html">electromagnetic wave</a>) when entering a different medium.
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<div class="def">
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<p>When electromagnetic waves enter a different medium the <b>speed changes</b>. The frequency stays the same, so the <b>wavelength must change</b>.</p>
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<p>This causes the <b>waves to change direction</b> (except when they travel directly forward):</p>
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<p class="center"><img src="images/refractions.gif" alt="refractions" height="138" width="400"></p>
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<p>See how the distance between pulses (the wavelength) changes, but the frequency of pulses stays the same.</p>
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</div>
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<p> </p>
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<div class="def">
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../geometry/images/normal-up.svg" alt="normal" height="161" width="119"></p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../geometry/images/normal.svg" alt="normal" height="141" width="114"></p>
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<p>Note: the "directly forward" direction is called the <b>Normal</b>.</p>
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<p>It is at <a href="../rightangle.html">right angles</a> to the surface.</p>
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<div style="clear:both"></div>
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</div>
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<p class="center"> </p>
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<h2>Going to a Denser Medium</h2>
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<p class="center larger def">The angle goes <b>towards</b> the normal on entering a <b>denser</b> medium.</p>
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<p class="center">Imagine marching in formation:</p>
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<p class="center"><img src="images/soldiers.gif" alt="soldiers marching" height="186" width="548"></p>
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<p class="center">And then going from <b>flat ground to a hill</b></p>
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<p class="center"><img src="images/refraction-marching.gif" alt="refraction marching at angle" height="235" width="240"><br>
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The pace slows down <b>on one side first</b>,<br>
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and to stay in ranks the <b>direction must change</b> a bit</p>
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<p class="center"><br>
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<img src="images/refraction-marching2.gif" alt="refraction marching straight ahead" height="183" width="240"><br>
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But the direction stays the same when marching straight up the hill </p>
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<h2>Going to a Less Dense Medium</h2>
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<p class="center larger def">The angle goes <b>away</b> from the normal on entering a <b>less dense</b> medium.</p>
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<p>Here we see both entering and leaving a denser medium:</p>
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<p class="center"><b>Towards normal</b> on entering <b>denser</b> medium<br>
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<img src="images/refraction-glass.gif" alt="refraction glass" height="209" width="180"><br>
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<b>Away from normal</b> on going to <b>less dense</b> medium.</p>
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<p><i>And because it returns to the same medium it returns to the same angle!</i></p>
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<p class="center">And here it is in real life, a ray of light being refracted in a plastic block.<br>
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<br>
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<img src="images/refraction-plastic-block.jpg" alt="refraction plastic block" height="227" width="240"><br>
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<i> The plastic is denser, so the light changes
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<b>towards normal</b> when entering<br>
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and changes <b>away from normal</b> on leaving.<br>
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Courtesy of wikipedia user ajizai</i></p>
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<p><br>
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And different shapes make for interesting effects:</p>
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<p class="center"><img src="images/refraction-glass-ball.jpg" alt="refraction glass ball" height="258" width="200"><br>
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The rays bunch up around the edge<br>
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<img src="images/refraction-globe.gif" alt="refraction globe" height="146" width="300"></p>
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<p>Our eyes use refraction to focus incoming light onto the back of our eye:</p>
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<p class="center"><img src="images/light-eye.gif" alt="light through eye" height="180" width="360"><br>
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Light refracts as it goes through our eyeballs,<br>
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That focuses the light beams at the back of our eye<br>
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where nerves detect the photons.<br>
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<i>Yes the image is upside down, but our eyes cope with that!</i></p>
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<h2>Refractive Index</h2>
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<p>The ratio of the <b>speed in a vacuum</b> to <b>speed in the medium</b> is called the Refractive Index (or Index of Refraction):</p>
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<p class="center large">n = <span class="intbl">
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<em>c</em>
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<strong>v</strong>
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</span></p>
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<p>where</p>
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<ul>
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<li><b>n</b> is the Refractive Index</li>
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<li><b>c</b> is the speed of light in vacuum and</li>
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<li><b>v</b> is the speed of light in the medium</li>
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</ul>
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<p><b>A bigger refractive index means a lower speed!</b></p>
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<div class="example">
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<h3>Example: the Refractive Index of water is 1.333</h3>
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<p>So light travels 1.333 times <b>slower</b> in water than in a vacuum</p>
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<ul>
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<li>Speed in a vacuum: 300,000 km/s</li>
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<li>Speed in water: 300,000 km/s / 1.333 = 225,000 km/s</li>
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</ul>
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</div>
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<p>Some Refractive Index values:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<th>Medium</th>
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<th align="center"><b>Speed</b><br>
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million m/s</th>
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<th align="center">Refractive Index<br>
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<b>n</b></th>
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</tr>
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<tr>
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<td>Vacuum</td>
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<td style="text-align:center;">299.8</td>
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<td style="text-align:center;">1</td>
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</tr>
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<tr>
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<td>Air</td>
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<td style="text-align:center;">299.7</td>
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<td style="text-align:center;">1.0003</td>
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</tr>
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<tr>
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<td>Ice</td>
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<td style="text-align:center;">228</td>
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<td style="text-align:center;">1.31 </td>
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</tr>
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<tr>
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<td>Water</td>
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<td style="text-align:center;">225</td>
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<td style="text-align:center;">1.333 </td>
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</tr>
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<tr>
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<td>Ethanol</td>
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<td style="text-align:center;">220</td>
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<td style="text-align:center;">1.36 </td>
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</tr>
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<tr>
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<td>Glass</td>
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<td style="text-align:center;">205</td>
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<td style="text-align:center;">1.46 </td>
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</tr>
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<tr>
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<td>Olive oil</td>
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<td style="text-align:center;">204</td>
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<td style="text-align:center;">1.47</td>
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</tr>
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<tr>
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<td>Diamond</td>
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<td style="text-align:center;">123</td>
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<td style="text-align:center;">2.42</td>
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</tr>
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</tbody></table></div>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/diamond.jpg" alt="diamond" height="189" width="239"></p>
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<p>The high refractive index of diamond causes the light to bounce around inside in interesting ways.</p>
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<p>When cut into the right shape by experts it will <i><b>sparkle</b></i>.</p>
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<div style="clear:both"></div>
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<h2>Critical Angle</h2>
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<p>At a certain angle (the Critical Angle) the ray starts to point back inside!</p>
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<p>The result is the light <b>reflects</b> back instead.</p>
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<p>It is called <b>Total Internal
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Reflection</b>:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="images/refract-a.gif" alt="refraction " height="163" width="160"></td>
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<td> </td>
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<td><img src="images/refract-b.gif" alt="refraction critical angle" height="163" width="160"></td>
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<td> </td>
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<td><img src="images/refract-c.gif" alt="reflection" height="162" width="160"></td>
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</tr>
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<tr style="text-align:center;">
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<td><b>Refraction</b></td>
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<td> </td>
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<td><b>Critical Angle</b></td>
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<td> </td>
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<td><b>Total Internal<br>
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Reflection</b></td>
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</tr>
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</tbody></table>
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<div class="example">
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<h3>Example: Water to Air</h3>
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<p>When looking from water to air we see the (usually 180° from horizon to horizon) world above the water
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as a <b>cone of about 96°</b>.</p>
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<p>Outside that 96° cone is a (much darker) reflection from the water below:</p>
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<p class="center"><img src="images/snells-window.jpg" alt="snells window diver" height="216" width="360"><br>
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<i>Navy Diver 2nd Class Ryan Arnold viewed from below</i></p>
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<p>Note also that the water surface is not flat, so it cause a local ripple effect.</p>
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</div>
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<p>Have a play with it:</p>
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<div class="script" style="height: 350px;">
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images/snell.js
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</div>
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<p>Try <i>Refraction Index 1 = 1</i>, <i>Refraction Index 2 = 1.33</i>, "<i>Down</i>" and "<i>Eye</i>" to create that effect of looking up from water.</p>
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<h2>Snell's Law</h2>
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<p>How do we calculate the angles? We use <b>Snell's Law</b>:</p>
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<p class="center large">n<sub>1</sub> sin(θ<sub>1</sub>) = n<sub>2</sub> sin(θ<sub>2</sub>)</p>
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<p>It works <b>up to the critical angle</b>, after that it is simple reflection:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td><b>n<sub>1</sub>sin(θ<sub>1</sub>) = n<sub>2</sub>sin(θ<sub>2</sub>)</b></td>
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<td> </td>
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<td><b>n<sub>1</sub>sin(θ<sub>crit</sub>) = n<sub>2</sub></b></td>
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<td> </td>
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<td><b>θ<sub>1</sub></b> = <b>θ<sub>1</sub></b></td>
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</tr>
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<tr style="text-align:center;">
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<td> </td>
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<td> </td>
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<td>because sin(90°)=1</td>
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<td> </td>
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<td>when θ<sub>1</sub> > θ<sub>crit</sub></td>
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</tr>
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<tr>
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<td><img src="images/refract-a.gif" alt="refraction " height="163" width="160"></td>
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<td> </td>
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<td><img src="images/refract-b.gif" alt="refraction critical angle" height="163" width="160"></td>
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<td> </td>
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<td><img src="images/refract-c.gif" alt="reflection" height="162" width="160"></td>
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</tr>
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<tr style="text-align:center;">
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<td><b>Refraction</b></td>
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<td> </td>
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<td><b>Critical Angle</b></td>
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<td> </td>
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<td><b>Total Internal<br>
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Reflection</b></td>
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</tr>
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</tbody></table>
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<div class="example">
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<h3>Example: What is the Critical Angle between air and water?</h3>
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<p>Index of Refraction of <b>air is 1.003</b>, and of <b>water is 1.333</b></p>
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<p>The Critical Angle is when <b>θ<sub>2</sub></b> is 90°</p>
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<div class="tbl">
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<div class="row"><span class="left">Start with:</span><span class="right">n<sub>1</sub> sin(θ<sub>1</sub>) = n<sub>2</sub> sin(θ<sub>2</sub>)</span></div>
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<div class="row"><span class="left">sin(90°) = 1, so:</span><span class="right">n<sub>1</sub> sin(θ<sub>1</sub>) = n<sub>2</sub></span></div>
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<div class="row"><span class="left">Divide both sides by n<sub>1</sub>:</span><span class="right">sin(θ<sub>1</sub>) = <span class="intbl">
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<em>n<sub>2</sub></em>
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<strong>n<sub>1</sub></strong>
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</span></span></div>
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<div class="row"><span class="left">Inverse sine:</span><span class="right">θ<sub>1</sub> = sin<sup>-1</sup>(<span class="intbl">
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<em>n<sub>2</sub></em>
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<strong>n<sub>1</sub></strong>
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</span>)</span></div>
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<div class="row"><span class="left">Put in the values:</span><span class="right">θ<sub>1</sub> = sin<sup>-1</sup>(<span class="intbl">
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<em>1.003</em>
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<strong>1.333</strong>
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</span>)</span></div>
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<div class="row"><span class="left">Calculate:</span><span class="right">θ<sub>1</sub> = 48.8°</span></div>
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</div>
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<p class="center">So <span class="center large">θ<sub>crit</sub> = 48.8°</span></p>
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</div>
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<p>You may prefer this form of Snell's Law, made by dividing both sides by sin(θ<sub>1</sub>) and n<sub>2</sub>:</p>
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<p class="center large"><span class="intbl">
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<em>n<sub>1</sub></em>
|
||
<strong>n<sub>2</sub></strong>
|
||
</span> = <span class="intbl">
|
||
<em>sin(θ<sub>2</sub>)</em>
|
||
<strong>sin(θ<sub>1</sub>) </strong>
|
||
</span></p>
|
||
<p>(Be careful though: <b>n</b> values go "1-over−2", but the <b>sin()</b> values go "2-over−1".)</p>
|
||
<p> </p>
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<div class="questions">17703, 17705, 17707, 17709, 17711, 17714, 17716, 17718, 17720, 17713</div>
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