davisnotes/lo_tir.html

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<title>Light and Optics - Total Internal Reflection - Physics 299</title>
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<h1><img src="ULPhys1.gif" align="texttop" height="50" width="189"></h1>
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<h1>Total Internal Reflection</h1>
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<center><img src="celticbar.gif" height="22" width="576"> <br>
<br>
<font color="#ff0000"><i>"One machine can do the work of fifty
ordinary men. &nbsp;No machine can do the work of one
extraordinary man"</i></font><br>
Elbert Hubbard<br>
</center>
<img src="netbar.gif" align="middle" height="40" width="100%"> <br>
<ul>
<li>When light passes from a medium with refractive index n<sub>1</sub>
to a medium with refractive index n<sub>2</sub>, where n<sub> 1</sub>
&gt; n<sub>2</sub>, if the incident angle is greater than some
critical angle <img alt="" src="lo_tir_eqn1.gif" style="width:
17px; height: 24px;" align="middle">, the light will undergo <i>
total internal reflection</i> (TIR).</li>
<br>
<li>The diagram below represents a light source underwater with
light rays striking the water-air interface. &nbsp;Rays 1, 2 and
3 are refracted at the interface according to Snell's law, the
refracted ray bending away from the normal such that&nbsp; <img
alt="" src="lo_tir_eqn3.gif" style="width: 19px; height:
23px;" align="middle">&nbsp; &gt; <img alt=""
src="lo_tir_eqn2.gif" style="width: 16px; height: 23px;"
align="middle"> . When <img alt="" src="lo_tir_eqn3.gif"
style="width: 19px; height: 23px;" align="middle"> = 90<sup>o</sup>
the refracted ray is directed along the surface of the water and
<img alt="" src="lo_tir_eqn2.gif" style="width: 16px; height:
23px;" align="middle"> is called the critical angle <img
alt="" src="lo_tir_eqn1.gif" style="width: 17px; height:
24px;" align="middle">. &nbsp;For incident angles greater than
<img alt="" src="lo_tir_eqn1.gif" style="width: 17px; height:
24px;" align="middle"> there is no refracted ray, the light
undergoes <i>total internal reflection</i> back into the water.</li>
</ul>
<blockquote><img alt="exclamation" src="exclamation-icon.gif"
height="30" width="31"> Note that even when TIR does not take
place there will always be a reflected wave (back into the water),
in this case, of low intensity (about 4% of the total energy is
reflected).&nbsp; In other words, at an interface where the
incident angle is less than the critical angle, part of the
incident energy is transmitted and part is reflected.<br>
</blockquote>
<ul>
<br>
<img alt="confused smiley" src="confused_smiley.gif" height="22"
width="15">&nbsp; Even though all the light energy undergoes
total internal reflection, there is a "disturbance" in the other
medium (air in the example above) called the evanescent wave which
travels along the interface between the two media...<br>
<div align="center"><img
src="lo_internalreflectiontwodiagrams.jpg" alt="TIR"
align="middle" height="235" width="570"> <br>
</div>
<li> At the critical angle<br>
<div align="center"><b><img alt="" src="lo_tir_eqn4.gif"
style="width: 131px; height: 89px;"> <br>
</b></div>
<br>
For light &nbsp;passing into air from water the critical angle
is equal to about 49<sup>o</sup>.&nbsp;</li>
<br>
<li>Thus a fish-eye's view is of the world in a 98<sup>o</sup>
cone. &nbsp;Outside this cone all is darkness...[Actually this
is not true due to the scattering of light in water] <br>
<div align="center"><img src="lo_coneofdarknessforfish.jpg"
alt="Fish view" align="middle" height="291" width="363"> <br>
</div>
</li>
<br>
<li> Total Internal Reflection is the mechanism by which fibre
optic cables work. &nbsp;Signal losses along such cables is
extremely small since <i><b> ALL</b></i> the incident energy is
reflected. <br>
<br>
<div align="center"><img
src="lo_fiberopticcladdingandfiberbundle.jpg" alt="Fibre
Optic" align="middle" height="185" width="570"> </div>
</li>
</ul>
<img src="netbar.gif" height="40" width="100%">
<center><span style="font-weight: normal; font-style: italic; color:
rgb(255, 0, 0);">"I know that this defies the law of gravity,
but, you see, I never studied</span><span style="font-style:
italic; color: rgb(255, 0, 0);"> law."</span><span style=""><br>
</span>Bugs Bunny <br>
<br>
<img src="celticbar.gif" height="22" width="576"></center>
<center> &nbsp; <br>
<i style="font-weight: normal;">Dr. C. L. Davis</i> <br>
<i style="font-weight: normal;">Physics Department</i> <br>
<i style="font-weight: normal;">University of Louisville</i> <br>
<i style="font-weight: normal;">email</i><span style="font-weight:
normal;">: </span><a style="font-weight: normal;"
href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a><span
style="font-weight: normal;"> </span><br>
&nbsp;
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