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fa-fw fa-chevron-right divider"></i></li><li><a href="../1128/ahl-waves.html">AHL Waves</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Thin film interference</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../waves/thin-film-bubble.jpg" style="float: left; width: 250px; height: 166px;">Bubbles in the air, peacock feathers in bloom and oily puddles all reveal a light phenomenon: thin film interference.</p> <p>It's a tricky concept involving reflection, refraction and phase changes at interfaces.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Phase changes at interfaces</p> </div> </div> <div class="panel-body"> <div> <p>When a wave reflects off a loose boundary, it experiences no phase change. However, when a wave reflects off a fixed boundary, it experiences a phase change of <span class="math-tex">\(\pi\)</span> radians.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369636632"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Conditions for interference</p> </div> </div> <div class="panel-body"> <div> <p>Thin film interference is a result of the combination of the different wavelengths of light and the different distances travelled through the film.</p> <p>The condition for constructive interference is:</p> <p style="text-align: center;"><span class="math-tex">\(2dn=(m+{1\over 2})\lambda\)</span></p> <ul> <li><span class="math-tex">\(d\)</span> is the thickness of the film (m)</li> <li><span class="math-tex">\(n\)</span> is the refractive index of the film</li> <li><span class="math-tex">\(m\)</span> is an integer value</li> <li><span class="math-tex">\(\lambda\)</span> is the wavelength of light (m)</li> </ul> <p>The condition for destructive interference is:</p> <p style="text-align: center;"><span class="math-tex">\(2dn=m\lambda\)</span></p> </div> </div> <div class="panel-footer"> <div> <div class="pinkBg"> <p> </p> </div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Thin film</p> </div> </div> <div class="panel-body"> <div> <p>When solving problems, take care to note what media are surrounding the film. A bubble consists of film between two laters of air.</p> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/waves/film-air.gif" style="width: 297px; height: 250px;"></p> <p>Oil on a surface has light arriving through air but water underneath.</p> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/waves/film-water.gif" style="width: 297px; height: 250px;"></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369636943"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Wedges of film</p> </div> </div> <div class="panel-body"> <div> <p>Since different wavelengths of light interfere constructively at different path differences, a variation in the thickness of a film will result in the appearance of bands of colour from an original white light source.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369637028"></iframe></div> <p>This effect can be used to test the flatness of manufactured glass surfaces.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#64312ed2"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="64312ed2"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Thin film interference <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-349-1124" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>The image, taken from a <span class="scayt-misspell-word" data-scayt-word="GeoGebra" data-wsc-lang="en_US">GeoGebra</span> simulation of thin film interference, shows a wave passing through a thin film.</p><p style="text-align: center;"><img alt="" height="153" src="../../waves/screenshot-2019-09-15-at-06.20.47.png" width="383"></p><p>The refractive index of the film is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>2</span></label> </p><p><label class="radio"> <input type="radio"> <span>3</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>4</span></label> </p><p><label class="radio"> <input type="radio"> <span>1.5</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(n = {c_1\over c_2} ={λ_1\over λ_2} = {6\over 1.5}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image, taken from a <span class="scayt-misspell-word" data-scayt-word="GeoGebra" data-wsc-lang="en_US">GeoGebra</span> simulation of thin film interference, shows a wave passing through a thin film.</p><p style="text-align: center;"><img alt="" height="153" src="../../waves/screenshot-2019-09-15-at-06.20.47.png" width="383"></p><p>If the wavelength of the wave in air is 400 nm, the thickness of the film is</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>4.0 μm</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.8 μm</span></label> </p><p><label class="radio"> <input type="radio"> <span>2.0 μm</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0.2 μm</span></label> </p></div><div class="q-explanation"><p>The wavelength in the film is <span class="math-tex">\(1\over 4\)</span> the wavelength in air = 100 nm.</p><p>Film is <span class="math-tex">\(2λ\)</span> thick = 200 nm = 200 x 10<sup>-9</sup> = 0.2 x 10<sup>-6</sup>.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image, taken from a <span class="scayt-misspell-word" data-scayt-word="GeoGebra" data-wsc-lang="en_US">GeoGebra</span> simulation of thin film interference, shows a wave passing through a thin film.</p><p style="text-align: center;"><img alt="" height="151" src="../../waves/screenshot-2019-09-15-at-06.56.55.png" width="343"></p><p>Which sequence gives the <span class="scayt-misspell-word" data-scayt-word="colours" data-wsc-lang="en_US">colours</span> of the waves in this order:</p><p>incident on 1st face - reflected off first face - reflected off second face</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>black - green - red</span></label> </p><p><label class="radio"> <input type="radio"> <span>red - green - black</span></label> </p><p><label class="radio"> <input type="radio"> <span>black - red - green</span></label> </p><p><label class="radio"> <input type="radio"> <span>green - red - black</span></label> </p></div><div class="q-explanation"><p>We see the green wave reflect off the left face out of phase.</p><p>The red wave reflects off the right face in phase.</p><p>The black line is incident on the left face and emergent from the right.</p><p>NB: Sorry if you are <span class="scayt-misspell-word" data-scayt-word="colour" data-wsc-lang="en_US">colour</span> blind - the exam would find a mechanism for distinguishing in black and white!</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image, taken from a <span class="scayt-misspell-word" data-scayt-word="GeoGebra" data-wsc-lang="en_US">GeoGebra</span> simulation of thin film interference, shows a wave passing through a thin film. The wavelength in the film is λ.</p><p style="text-align: center;"><img alt="" height="151" src="../../waves/screenshot-2019-09-15-at-06.56.55.png" width="343"></p><p>The path difference between the red and green waves is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>2λ</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>4λ</span></label> </p><p><label class="radio"> <input type="radio"> <span>4.5λ</span></label> </p><p><label class="radio"> <input type="radio"> <span>2.5λ</span></label> </p></div><div class="q-explanation"><p>The path difference = 2 x thickness.</p><p>In this case, the thickness coincides with being 2λ.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image, taken from a <span class="scayt-misspell-word" data-scayt-word="GeoGebra" data-wsc-lang="en_US">GeoGebra</span> simulation of thin film interference, shows a wave passing through a thin film.</p><p style="text-align: center;"><img alt="" height="151" src="../../waves/screenshot-2019-09-15-at-06.56.55.png" width="343"></p><p>The phase difference between the green and red waves is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(4π\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(9π\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(8.5π\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(8π\)</span></span></label></p></div><div class="q-explanation"><p>At the left boundary, the green wave reflects with <span class="math-tex">\(\pi\)</span> phase difference to the black wave that enters. The red wave has travelled two wavelengths towards the right boundary and two wavelengths back to the left. Each wavelength contributes a further <span class="math-tex">\(2\pi\)</span> phase difference. The total is <span class="math-tex">\(9\pi\)</span>.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A parallel sided soap film of thickness 0.01 μm is illuminated with light of wavelength 700 nm.</p><p>The appearance of the film is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>a series of red lines</span></label> </p><p><label class="radio"> <input type="radio"> <span>white</span></label> </p><p><label class="radio"> <input type="radio"> <span>red</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>black</span></label> </p></div><div class="q-explanation"><p>The film thickness (<span class="math-tex">\(10^{-8} \text { m}\)</span>) is much less than the wavelength of the light (almost <span class="math-tex">\(10^{-6} \text{ m}\)</span>) so the path difference is negligible. The phase difference is therefore <span class="math-tex">\(\approx \pi\)</span> so the waves cancel.</p><p>Lines are formed by wedges of film with continuously changing thickness.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The thickness of a soap bubble reduces as the soap drains from it. What is the minimum value of the product of thickness and refractive index for constructive interference of light of wavelength 600 nm?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>600 nm</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>150 nm</span></label> </p><p><label class="radio"> <input type="radio"> <span>1200 nm</span></label> </p><p><label class="radio"> <input type="radio"> <span>300 nm</span></label> </p></div><div class="q-explanation"><p>Constructive interference occurs when <span class="math-tex">\(2dn=(m+{1\over 2})\lambda\)</span>. Reducing the right hand side using integer <span class="math-tex">\(m=1\)</span>:</p><p><span class="math-tex">\(dn={1\over4}λ\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image represents a wave passing into a more dense medium.</p><p style="text-align: center;"><img alt="" height="369" src="../../waves/screenshot-2019-09-15-at-08.01.40.png" width="255"></p><p>The reflected wave that has been produced in the same time frame is best represented by:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>D</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>B</span></label> </p><p><label class="radio"> <input type="radio"> <span>C</span></label> </p><p><label class="radio"> <input type="radio"> <span>A</span></label> </p></div><div class="q-explanation"><p>What was a trough is reflected as a peak.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image represents a wave passing into a less dense medium.</p><p style="text-align: center;"><img alt="" height="369" src="../../waves/screenshot-2019-09-15-at-08.01.40.png" width="255"></p><p>The reflected wave that has been produced in the same time frame is best represented by:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>A</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>C</span></label> </p><p><label class="radio"> <input type="radio"> <span>D</span></label> </p><p><label class="radio"> <input type="radio"> <span>B</span></label> </p></div><div class="q-explanation"><p>What was a trough is reflected as a trough.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container 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