File "markscheme-HL-paper3.html"
Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Physics/Topic 9 HTML/markscheme-HL-paper3html
File size: 334.76 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-212ef6a30de2a281f3295db168f85ac1c6eb97815f52f785535f1adfaee1ef4f.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-13d27c3a5846e837c0ce48b604dc257852658574909702fa21f9891f7bb643ed.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../index.html">Home</a>
</li>
<li class="active dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Questionbanks
<b class="caret"></b>
</a><ul class="dropdown-menu">
<li>
<a href="../../geography.html" target="_blank">DP Geography</a>
</li>
<li>
<a href="../../physics.html" target="_blank">DP Physics</a>
</li>
<li>
<a href="../../chemistry.html" target="_blank">DP Chemistry</a>
</li>
<li>
<a href="../../biology.html" target="_blank">DP Biology</a>
</li>
<li>
<a href="../../furtherMath.html" target="_blank">DP Further Mathematics HL</a>
</li>
<li>
<a href="../../mathHL.html" target="_blank">DP Mathematics HL</a>
</li>
<li>
<a href="../../mathSL.html" target="_blank">DP Mathematics SL</a>
</li>
<li>
<a href="../../mathStudies.html" target="_blank">DP Mathematical Studies</a>
</li>
</ul></li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="images/ib-qb-46-logo-683ef0176708d789b2acbf6ece48c55de4cd5ddac781fb455afe3540d22d050e.jpg" alt="Ib qb 46 logo">
</div>
</div>
</div><h2>HL Paper 3</h2><div class="specification">
<p class="p1">This question is about thin-film interference.</p>
<p class="p1">The diagram (not to scale) represents an experimental set-up designed to measure the diameter of a human hair.</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2016-11-10_om_10.28.51.png" alt="N10/4/PHYSI/HP3/ENG/TZ0/G5"></p>
<p class="p1">A hair is used to separate two microscope slides. A monochromatic beam of light is reflected onto the two slides by the glass plate. The light is then reflected from the two slides and transmitted through the glass plate and is viewed by the travelling microscope.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State why the light reflected from the two microscope slides produces a system of interference fringes.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The condition that a bright fringe is observed in the field of view of the travelling microscope is given by the relationship</p>
<p class="p1">\[2t = \left( {m + \frac{1}{2}} \right)\lambda \]</p>
<p class="p1">where \(t\) is the thickness of the air film formed by the wedge at the point where the bright fringe is observed, \(m\) is an integer and \(\lambda \) is the wavelength of the incident light.</p>
<p class="p1">State the reason for the factor \(\frac{1}{2}\) in the relationship.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">In the diagram, the length of the slides is 5.00 cm. The wavelength of the monochromatic light is \(5.92 \times {10^{ - 7}}{\text{ m}}\). Using the travelling microscope it is observed that 50 fringes occupy a length of 0.940 cm. Show that the diameter of the hair used to separate the slides is about \({\text{80 }}\mu {\text{m}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">light reflected from the top slide interferes with light reflected from the bottom slide;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">the light reflected from the bottom slide undergoes a \(\pi \) change in phase;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">in moving from one (bright) fringe to the next the thickness of the air film changes by \(\frac{\lambda }{2}\);</p>
<p class="p1">in 5.0 cm number of fringes \( = \frac{5}{{0.940}} \times 50 = 266\);</p>
<p class="p1">therefore diameter of hair \( = 133 \times 5.92 \times {10^{ - 7}} = 7.87 \times {10^{ - 5}}{\text{ m}}\);</p>
<p class="p1">\(80{\text{ }}\mu {\text{m}}\)</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">A significant number of candidates did not attempt this question or made very poor attempts at answering.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">A significant number of candidates did not attempt this question or made very poor attempts at answering.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">A significant number of candidates did not attempt this question or made very poor attempts at answering. Candidates who gave good answers often used, correctly, a similar triangles approach to determining the diameter of the hair in part (c).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about thin-film interference.</p>
<p><br>A thin film of oil lies on a puddle of water. White light from above shines on the film at normal incidence.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the process by which coloured fringes are formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following data are available:</p>
<p style="padding-left: 30px;">Refractive index of oil = 1.4<br>Refractive index of water = 1.3<br>Thickness of the oil film = 250 nm</p>
<p>Calculate the maximum wavelength of the incident light for which <strong>destructive</strong> interference occurs.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 12">
<div class="layoutArea">
<div class="column">
<p><span style="font-size: 11.000000pt; font-family: 'Arial';">light reflects from the top surface of the oil and the top surface of the water;<br>mention of interference/superposition;<br>path difference exists between both reflected rays;<br> different wavelengths interfere constructively for different positions/angles (hence colours appear/shift); </span></p>
</div>
</div>
</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 12">
<div class="layoutArea">
<div class="column">
<p><span style="font-size: 11.000000pt; font-family: 'Arial';">\(\lambda \left( { = t\frac{{2n}}{m}} \right) = 250 \times {10^{ - 9}}\frac{{2 \times 1.4}}{1}\);<br>\(\lambda = 700\left( {{\rm{nm}}} \right)\);</span></p>
</div>
</div>
</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about thin-film interference.</p>
<p class="p1">A thin film of oil of constant thickness floats on the surface of water. The refractive indices \(n\) of each material is shown on the diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-09-02_om_05.23.58.png" alt="N14/4/PHYSI/HP3/ENG/TZ0/15"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why the film of oil appears to show coloured fringes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">When white light is normally incident on the surface of the oil, the film appears green to an observer. The wavelength of green light in air is 520 nm. Calculate the thickness of the film of oil.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">the light reflects at the air<span class="s1">:</span>oil and the oil<span class="s1">:</span>water boundary; <em>(can be shown on </em><em>diagram)</em></p>
<p class="p1">light reflecting from the oil<span class="s1">:</span>water boundary interferes with the light reflecting from the air<span class="s1">:</span>oil boundary;</p>
<p class="p1">depending on the thickness of the oil, different frequencies show constructive/destructive interference (hence coloured fringes);</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><em>for constructive interference</em>:</p>
<p class="p1">\(\left( {2nt = \left[ {m + \frac{1}{2}} \right]\lambda } \right)\)</p>
<p class="p1">\(t = \left[ {m + \frac{1}{2}} \right]\frac{\lambda }{{2n}}\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)\(\left[ {0 + \frac{1}{2}} \right]\frac{{520 \times {{10}^{ - 9}}}}{{2 \times 1.40}}\);</p>
<p class="p1">\(t = 93{\text{ nm}}\);</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">A large number of candidates did not explain two reflected rays, and that interference was dependent on the thickness of the oil film.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">A large number of candidates did not explain two reflected rays, and that interference was dependent on the thickness of the oil film.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph below represents the variation with time <em>t </em>of the horizontal displacement <em>x </em>of a mass attached to a vertical spring.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_15.49.15.png" alt="M18/4/PHYSI/HP3/ENG/TZ1/11"></p>
</div>
<div class="specification">
<p>The total mass for the oscillating system is 30 kg. For this system</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the motion of the spring-mass system.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>determine the initial energy.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>calculate the Q at the start of the motion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>damped oscillation / <em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em> <strong>«</strong><span class="Apple-converted-space">= \(\frac{1}{2}\) × 30 × <em>π</em><sup>2</sup> × 0.8<sup>2</sup></span><strong>»</strong> = 95 <strong>«</strong><span class="Apple-converted-space">J</span><strong>»</strong></p>
<p> </p>
<p><em>Allow initial amplitude between 0.77 to 0.80, giving range between: 88 to 95 J.</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>E</em> = 95 – \(\frac{1}{2}\) × 30 × <em>π</em><sup>2</sup> × 0.72<sup>2</sup> = 18 <strong>«</strong><span class="Apple-converted-space">J</span><strong>»</strong></p>
<p><em>Q = </em><strong>«</strong><span class="Apple-converted-space"> 2<em>π</em>\(\frac{{95}}{{18}}\) =</span><strong>»</strong> 33</p>
<p> </p>
<p><em>Accept values between 0.70 and 0.73, giving a range of</em> Δ<em>E between 22 and 9, giving Q between 27 and 61.</em></p>
<p><em>Watch for ECF from (b)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about thin-film interference.</p>
<p class="p1">A thin layer of oil of refractive index 1.51 floats on water of refractive index 1.33. Light of wavelength 579 nm is incident normally to the surface.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-09-08_om_12.52.32.png" alt="M14/4/PHYSI/HP3/ENG/TZ2/14"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine the minimum thickness of the oil layer that gives rise to the least amount of light being reflected.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Describe the change in the intensity of the reflected light as the thickness of the oil layer in (a) is gradually increased.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">use of \(m = 1\);</p>
<p class="p1">\(2 \times 1.51 \times t = 1 \times 579 \times {10^{ - 9}}\);</p>
<p class="p1">\(t = 1.92 \times {10^{ - 7}}{\text{ (m)}}\);</p>
<p class="p1"><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer.</em></p>
<p class="p1"><em>Award </em><strong><em>[2 max] </em></strong><em>for use of </em>\(m = \frac{1}{2}\)<em> giving 9.6 </em>\( \times \)<em> 10<sup>–8</sup> (m).</em></p>
<p class="p1"><em>Award </em><strong><em>[2 max] </em></strong><em>for answer of </em>\(\frac{\lambda }{2}\)<em> for air (2.9 </em>\( \times \)<em> 10<sup>–7</sup> (m)).</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">intensity increases;</p>
<p class="p1">intensity then decreases and increases repeatedly;</p>
<p class="p1">when thickness becomes very large the intensity becomes constant;</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">In (a) the correct thin film formula from the data booklet was sometimes chosen, but many candidates were able to answer the question using first principles. A common mistake was was to give the half wavelength value in air rather than oil or to forget the phase change on the hard reflection.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Few could give a well reasoned answer to (b) and were often lucky to score one mark.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about thin-film interference.</p>
<p class="p1">Monochromatic light with wavelength 572 nm is incident from air on a thin soap film.</p>
<p class="p1">The soap solution has a refractive index of 1.3.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-08-30_om_07.50.38.png" alt="N15/4/PHYSI/HP3/ENG/TZ0/11"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the wavelength of the light within the soap solution.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the minimum thickness of the soap film that results in constructive interference for the reflected light.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Without a calculation, explain why a soap film that is twice as thick as that calculated in (b) results in destructive interference.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\lambda ' = \frac{\lambda }{{1.33}} = \frac{{572}}{{1.3}} = 440{\text{ nm}}\);</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">110 nm;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">there would be a full wavelength within the film;</p>
<p class="p1">but the phase change at the first surface means that there is always destructive interference;</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Vast majority of candidates calculated the values well and also explained destructive interference properly.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Vast majority of candidates calculated the values well and also explained destructive interference properly.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Vast majority of candidates calculated the values well and also explained destructive interference properly.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about wedge fringes.</p>
<p>A glass microscope slide of length 6.0cm is placed on a glass plate and illuminated using a monochromatic source of light of wavelength 590nm. A hair is trapped at one end of the slide forming an air wedge between the glass plate and the slide.</p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question">
<p>An observer viewing the microscope slide at near-normal incidence measures the fringe spacing to be 0.29 mm. Calculate the thickness of the hair.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>there are \(\frac{{60}}{{0.29}}\) fringes=207;<br>2×1×<em>t</em>=207×5.9×10<sup>-7</sup>;<br><em>t</em>=61(μm);</p>
<p><em><strong>or</strong></em></p>
<p>\(\left( {\tan \theta = } \right)\frac{1}{{6.0\left( {{\rm{cm}}} \right)}} = \frac{{0.5\lambda }}{{\Delta x}}\);<br>\(t = \frac{{\left[ {0.06\left( {\rm{m}} \right) \times 0.5 \times 5.9 \times {{10}^{ - 7}}\left( {\rm{m}} \right)} \right]}}{{0.00029\left( {\rm{m}} \right)}}\);<br><em>t</em>=61(μm);<br><em>A phase change of \(\frac{1}{2}\lambda \), if seen in working, can be ignored and does not affect </em><em>the answer.</em><br><em>Award<strong> [3]</strong> for a bald correct answer.</em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>This question is about wedge film interference.</p>
<p>One flat, glass slide is placed at an angle on top of a second identical slide. The slides are in contact along one short edge and are separated at the other edge by a thin piece of paper, as shown below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
<p style="text-align: left;">A thin wedge of air of variable thickness, <em>t</em> , is trapped between the two slides. The arrangement is viewed normally from above, using light of wavelength 590 nm. The glass plates are coated, so that reflection only takes place at the bottom surface of the top plate and the top surface of the bottom plate.</p>
<p style="text-align: left;">A series of straight bright and dark fringes, equally separated and parallel to the short edge of the slides, is seen.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that the thickness of the air wedge <em>t</em> that gives rise to a bright fringe, is given by \(2t = (m + \frac{1}{2})\lambda \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The length of the air wedge,<em> L</em>, is 8.2 cm. The bright fringes are each separated by a distance of 1.2 mm. Calculate the thickness of the paper.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>phase change of <em>π</em> occurs on reflection at one slide but not the other;<br>constructive interference occurs when path difference between two reflected rays is \(\frac{\lambda }{2},\frac{{3\lambda }}{2},\frac{{5\lambda }}{2}\) etc;<br>the extra distance travelled is twice the thickness of the air (wedge) hence 2<em>t</em> = [<em>m</em>+½] λ;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>number of fringes = \(\frac{{82}}{{1.2}} = 68\);<br>fringe separation corresponds to a change in thickness of \(\frac{\lambda }{2}\);<br>thickness of paper\( = 68 \times \frac{{590 \times {{10}^{ - 9}}}}{2} = 2.0 \times {10^{ - 5}}{\rm{m}}\);</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about wedge films.</p>
<p>The diagram shows two thin glass plates used to form a thin air wedge.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>A beam of monochromatic light is incident on the air wedge. The reflected light is observed through a microscope and a pattern of equally spaced parallel fringes is observed.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the fringes are formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain how the fringe separation changes if the angle of the wedge is increased slightly.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>fringes arise as a result of interference between light reflected from top and bottom plates;<br>there is a phase difference of \(\pi \) at bottom reflection;<br>hence constructive interference when 2<em>d</em>=(<em>n</em>+½)λ and destructive when 2<em>d</em>=<em>n</em>λ;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the fringe separation would decrease;<br>the distance between the points/places/positions where the light is in phase or antiphase would be shorter;</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about thin-film interference.</p>
<p>A piece of glass of refractive index 1.62 is covered with a thin film of magnesium fluoride of thickness <em>t</em> and refractive index 1.38. The diagram shows a ray of monochromatic light incident on the film at an angle <em>θ</em> to the normal.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
<p style="text-align: left;">X is a ray reflected from the surface of the film and Y is reflected from the surface of the glass.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that when <em>θ</em>=0 the condition for destructive interference between rays X and Y is</p>
<p style="text-align: center;">2<em>t</em>=(m+½)<em>λ</em></p>
<p style="text-align: left;">where <em>m</em> is an integer and <em>λ</em> is the wavelength of light in the magnesium fluoride film.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Light of wavelength 640 nm in air is incident normally on the glass surface.</p>
<p>(i) Show that the wavelength of light in the magnesium fluoride film is 464 nm.</p>
<p>(ii) Calculate the minimum thickness of the film for which no light will be reflected back into the air.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the path difference (at normal incidence) is 2<em>t</em>;<br>since there is phase change of π at both surfaces there is destructive interference if the path difference is half integral multiple of the wavelength;<br>and so 2<em>t</em>=(m+½)<em>λ</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \(\lambda = \frac{{{\lambda _{{\rm{air}}}}}}{n} = \frac{{640}}{{1.38}}\);<br>=464nm</p>
<p>(ii) \(m = 0 \Rightarrow t = \frac{\lambda }{4}\);<br>\(t = \left( {\frac{{464}}{4} = } \right)116{\rm{nm}} \approx 120{\rm{nm}}\);</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 6">
<div class="layoutArea">
<div class="column">
<div class="page" title="Page 1">
<div class="layoutArea">
<div class="column">
<p> </p>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 6">
<div class="layoutArea">
<div class="column">
<div class="page" title="Page 1">
<div class="layoutArea">
<div class="column">
<p> </p>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about thin-film interference.</p>
<p>The anti-reflective coating of a lens consists of a thin layer of a suitable material placed between the air and the glass of the lens.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p> </p>
<p>The following data are available.</p>
<p style="text-align: left;"> Refractive index of air = 1.0<br> Refractive index of coating = 1.2<br> Refractive index of glass = 1.5</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what phase change occurs on reflection at the air-coating boundary and at the coating-glass boundary.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thickness <em>d</em> of the coating layer is 110 nm.</p>
<p>Determine the wavelength for which there is no resultant reflection from the surface of the lens for light at normal incidence <em>(θ = 0º</em> ).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>180º / <em>π;</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>path difference must be \(\frac{\lambda }{2}\);</p>
<p>physical thickness must be \(\frac{\lambda }{2n}\);</p>
<p>so, maximum wavelength \(\left( {{\rm{is}}\left[ {2nt = \left[ {m + \frac{1}{2}} \right]\lambda } \right] \to \lambda = 4{n_c}d} \right) = 528\left( {{\rm{nm}}} \right)\);</p>
<p><em>Allow any valid alternative method.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>was well done in general</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Was poorly understood. There were some good answers but many candidates omitted <em>n</em> or put <em>n</em> = 1 as in a diffraction grating.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about thin-film interference.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A ray of monochromatic light is incident on a thin film of soap water that is suspended in air. The diagram shows the reflection of this ray from the top and bottom surfaces of the film.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>On the diagram, label, with the letter P, the point at which a phase difference of \(\pi \) occurs.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>White light is incident normally on the soap film. The thickness <em>d</em> of the soap film is 225 nm and its refractive index is 1.34.</p>
<p>(i) Show that the longest wavelength of light<em> λ</em> in air for which the reflected rays destructively interfere is 603 nm.</p>
<p>(ii) Explain why the soap film will appear coloured.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p> </p>
<p>P as shown;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) for destructive interference, use of 2<em>μd</em>=<em>nλ</em> to give <em>λ</em>=2<em>μd</em> (<em>ie n</em>=1);<br><em>λ</em>=2×1.34×225;<br>(603nm)<br><em>Answer given, look for correct working.</em></p>
<p>(ii) the reflected light is white minus the wavelengths that suffer destructive interference;<br>some colours are determined by the missing wavelengths;<br>some colours are enhanced due to constructive interference; </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>There is considerable uncertainty amongst candidates about the surface at which a phase change occurs on reflection.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(b)(i) was an easy two marks for most. However (b)(ii) was poorly answered. More often than not only refraction, diffraction or dispersion were mentioned - even though the G5 question was clearly indicated as being about thin film interference. It is very good practice for candidates to read the stem of the question carefully before starting, and to highlight key phrases or data.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about thin-film interference.</p>
<p>A thin air wedge consists of two flat glass plates that form an angle <em>θ</em> of 1.0×10<sup>–3</sup>rad.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>When illuminated with monochromatic light from above, the fringe pattern below is observed in the reflected light. The distance <em>D</em> between two consecutive fringes is 0.30mm.</p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the light.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The upper glass plate is now replaced with a curved glass plate. The dotted line represents the upper glass plate used in (a).</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Sketch the new fringe pattern in the space below. The fringe pattern of (a) is given for comparison.</p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\lambda = \left( {2D\tan \theta = } \right)2 \times 0.30\tan {10^{ - 3}}\) <em><strong>or</strong></em> \(2 \times 0.30\sin {10^{ - 3}}\);<br>\(\lambda = 6.0 \times {10^{ - 7}}\left( {\rm{m}} \right)\);<br><em>Award <strong>[1 max]</strong> for use of degrees instead of radians giving \(\lambda = 1.0 \times {10^{ - 8}}\left( {\rm{m}} \right)\).</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreasing distance from left to right;<br>distance larger than original at left and shorter than original at right;</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiYAAAIACAYAAAC2O6dtAAAKqGlDQ1BJQ0MgUHJvZmlsZQAASImVlwdUFEkax6u7JwfSwEhmiEOQnEFyHILkaGKYIQxhGAYGFTOyqOAaUBEBRdBVEAVXJYgJEcW0CAYw7yCLiHouBkyocw0cw+3du7t3//fq1a+/rv7q6+qq9/4NAOUqWyDIgOUAyOTnCsP9PBmxcfEMvBggAA+IgAQgNidH4BEaGgRQzfR/1cd+AE32d0wnc/37/f8qeW5SDgcAKBTlRG4OJxPlU2g7zhEIcwFAuGhcd2muYJI3oqwoRAtEuWqSU6b5+CQnTnPX1JjIcC+U7wNAoLDZwhQAyH+gcUYeJwXNQ8GgbMHn8vgo26Dsykllo/NQ0HtgbmZm1iTvR9kw8Z/ypPwlZ6I0J5udIuXpd5kSwZuXI8hgL/8/l+N/KzNDNDOHDtooqUL/8Mn50DWrS88KlDI/cX7IDPO40zVNcqrIP2qGOTle8TPMZXsHzrAoPcpjhtnC2Wd5uazIGRZmhUvz8zPmB0nzJ7GknJTjEzHDyTxf1gznp0bGzHAeL3r+DOekRwTOjvGSxoWicGnNyUJf6Ttm5szWxmHPzpWbGuk/W0OstB5ukrePNM6Pko4X5HpKcwoyQmfrz/CTxnPyIqTP5qIbbIbT2AGhs3lCpesDeCAYsAEnN2nZ5L4CXlmC5UJeSmouwwM9JUkMFp9jNpdhZWFpB8DkmZv+pO/pU2cJol+fja1vBsDlvEQiOTMbC9wGwEkmAKTe2RhzOwCyagBcreGIhHnTscmtDrDoOZYFikAFaAJdYAhMgRWwA87AHfiAABACIkEcWAw4IBVkAiFYClaCdaAIlIBtYBeoANXgAKgDx8AJ0ArOgovgCrgBesE98AiIwTB4BcbARzABQRAeokI0SAXSgvQhE8gKcoBcIR8oCAqH4qAEKAXiQyJoJbQeKoFKoQqoBqqHfoVOQxeha1Af9AAahEahd9BXGIEpsCKsARvA5rAD7AEHwpHwIjgFzobz4UJ4C1wO18JH4Rb4InwDvgeL4VfwOAIQMkJHtBFTxAHxQkKQeCQZESKrkWKkDKlFGpF2pBu5g4iR18gXDA5DwzAwphhnjD8mCsPBZGNWYzZjKjB1mBZMF+YOZhAzhvmBpWLVsSZYJywLG4tNwS7FFmHLsIewzdjL2HvYYexHHA5HxzFx9jh/XBwuDbcCtxm3F9eE68D14YZw43g8XgVvgnfBh+DZ+Fx8EX4P/ij+Av42fhj/mUAmaBGsCL6EeAKfUEAoIxwhnCfcJowQJohyRH2iEzGEyCUuJ24lHiS2E28Rh4kTJHkSk+RCiiSlkdaRykmNpMukx6T3ZDJZh+xIDiPzyGvJ5eTj5KvkQfIXigLFmOJFWUgRUbZQDlM6KA8o76lUqgHVnRpPzaVuodZTL1GfUj/L0GTMZFgyXJk1MpUyLTK3Zd7IEmX1ZT1kF8vmy5bJnpS9JftajihnIOclx5ZbLVcpd1puQG5cniZvKR8inym/Wf6I/DX5Fwp4BQMFHwWuQqHCAYVLCkM0hKZL86JxaOtpB2mXacOKOEWmIksxTbFE8Zhij+KYkoKSjVK00jKlSqVzSmI6Qjegs+gZ9K30E/R++tc5GnM85iTN2TSncc7tOZ+U1ZTdlZOUi5WblO8pf1VhqPiopKtsV2lVeaKKUTVWDVNdqrpP9bLqazVFNWc1jlqx2gm1h+qwurF6uPoK9QPqN9XHNTQ1/DQEGns0Lmm81qRrumumae7UPK85qkXTctXiae3UuqD1kqHE8GBkMMoZXYwxbXVtf22Rdo12j/aEDlMnSqdAp0nniS5J10E3WXenbqfumJ6WXrDeSr0GvYf6RH0H/VT93frd+p8MmAYxBhsMWg1eMJWZLGY+s4H52JBq6GaYbVhreNcIZ+RglG6016jXGDa2NU41rjS+ZQKb2JnwTPaa9M3FznWcy59bO3fAlGLqYZpn2mA6aEY3CzIrMGs1e2OuZx5vvt282/yHha1FhsVBi0eWCpYBlgWW7ZbvrIytOFaVVnetqda+1mus26zf2pjYJNnss7lvS7MNtt1g22n73c7eTmjXaDdqr2efYF9lP+Cg6BDqsNnhqiPW0dNxjeNZxy9Odk65Tiec/nQ2dU53PuL8Yh5zXtK8g/OGXHRc2C41LmJXhmuC635XsZu2G9ut1u2Zu6471/2Q+4iHkUeax1GPN54WnkLPZs9PXk5eq7w6vBFvP+9i7x4fBZ8onwqfp746vim+Db5jfrZ+K/w6/LH+gf7b/QdYGiwOq541FmAfsCqgK5ASGBFYEfgsyDhIGNQeDAcHBO8Ifjxffz5/fmsICGGF7Ah5EsoMzQ49E4YLCw2rDHsebhm+Mrw7ghaxJOJIxMdIz8itkY+iDKNEUZ3RstELo+ujP8V4x5TGiGPNY1fF3ohTjePFtcXj46PjD8WPL/BZsGvB8ELbhUUL+xcxFy1bdG2x6uKMxeeWyC5hLzmZgE2ISTiS8I0dwq5ljyeyEqsSxzhenN2cV1x37k7uaJJLUmnSSLJLcmnyixSXlB0po6luqWWpr3levAre2zT/tOq0T+kh6YfTJRkxGU2ZhMyEzNN8BX46vytLM2tZVp/ARFAkEGc7Ze/KHhMGCg/lQDmLctpyFVFzc1NkKPpJNJjnmleZ93lp9NKTy+SX8ZfdXG68fNPykXzf/F9WYFZwVnSu1F65buXgKo9VNauh1YmrO9forilcM7zWb23dOtK69HW/FVgUlBZ8WB+zvr1Qo3Bt4dBPfj81FMkUCYsGNjhvqN6I2cjb2LPJetOeTT+KucXXSyxKykq+beZsvv6z5c/lP0u2JG/p2Wq3dd823Db+tv7tbtvrSuVL80uHdgTvaNnJ2Fm888OuJbuuldmUVe8m7RbtFpcHlbft0duzbc+3itSKe5WelU1V6lWbqj7t5e69vc99X2O1RnVJ9df9vP33a/xqWmoNassO4A7kHXh+MPpg9y8Ov9QfUj1Ucuj7Yf5hcV14XVe9fX39EfUjWxvgBlHD6NGFR3uPeR9razRtrGmiN5UcB8dFx1/+mvBr/4nAE50nHU42ntI/VdVMay5ugVqWt4y1praK2+La+k4HnO5sd25vPmN25vBZ7bOV55TObT1POl94XnIh/8J4h6Dj9cWUi0OdSzofXYq9dLcrrKvncuDlq1d8r1zq9ui+cNXl6tlrTtdOX3e43nrD7kbLTdubzb/Z/tbcY9fTcsv+VluvY29737y+87fdbl+8433nyl3W3Rv35t/r64/qvz+wcEB8n3v/xYOMB28f5j2ceLT2MfZx8RO5J2VP1Z/W/m70e5PYTnxu0Hvw5rOIZ4+GOEOv/sj549tw4XPq87IRrZH6F1Yvzo76jva+XPBy+JXg1cTror/J/63qjeGbU3+6/3lzLHZs+K3wreTd5vcq7w9/sPnQOR46/vRj5seJT8WfVT7XfXH40v015uvIxNJv+G/l342+t/8I/PFYkimRCNhC9pQVQNAGJycD8O4wANQ4AGi9qH+QmfbEU4KmffwUgf/E0755SqhzaUS7SSvk1QHAcbQZuAMgg15PWqJIdwBbW0vbP5STbG01nYuCOkvsZ4nkvQYA+HYAvgslkom9Esn3g2ixDwDoyJ724pPCoX8ojXhXjveCvnbzteBf9HcIWQN53PJn6wAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAxppVFh0WE1MOmNvbS5hZG9iZS54bXAAAAAAADx4OnhtcG1ldGEgeG1sbnM6eD0iYWRvYmU6bnM6bWV0YS8iIHg6eG1wdGs9IlhNUCBDb3JlIDUuNC4wIj4KICAgPHJkZjpSREYgeG1sbnM6cmRmPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5LzAyLzIyLXJkZi1zeW50YXgtbnMjIj4KICAgICAgPHJkZjpEZXNjcmlwdGlvbiByZGY6YWJvdXQ9IiIKICAgICAgICAgICAgeG1sbnM6dGlmZj0iaHR0cDovL25zLmFkb2JlLmNvbS90aWZmLzEuMC8iCiAgICAgICAgICAgIHhtbG5zOmV4aWY9Imh0dHA6Ly9ucy5hZG9iZS5jb20vZXhpZi8xLjAvIj4KICAgICAgICAgPHRpZmY6T3JpZW50YXRpb24+MTwvdGlmZjpPcmllbnRhdGlvbj4KICAgICAgICAgPHRpZmY6WVJlc29sdXRpb24+MTQ0PC90aWZmOllSZXNvbHV0aW9uPgogICAgICAgICA8dGlmZjpSZXNvbHV0aW9uVW5pdD4yPC90aWZmOlJlc29sdXRpb25Vbml0PgogICAgICAgICA8dGlmZjpDb21wcmVzc2lvbj4xPC90aWZmOkNvbXByZXNzaW9uPgogICAgICAgICA8dGlmZjpQaG90b21ldHJpY0ludGVycHJldGF0aW9uPjI8L3RpZmY6UGhvdG9tZXRyaWNJbnRlcnByZXRhdGlvbj4KICAgICAgICAgPHRpZmY6WFJlc29sdXRpb24+MTQ0PC90aWZmOlhSZXNvbHV0aW9uPgogICAgICAgICA8ZXhpZjpQaXhlbFhEaW1lbnNpb24+NTUwPC9leGlmOlBpeGVsWERpbWVuc2lvbj4KICAgICAgICAgPGV4aWY6UGl4ZWxZRGltZW5zaW9uPjUxMjwvZXhpZjpQaXhlbFlEaW1lbnNpb24+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgrnbjvZAAApo0lEQVR4Ae3dC5RlZXUn8K8AJ4CM3dDMaHRm0YqKSUyorNHhFeySJGMi4IsRfEUxy8AyM46OyShECa3RBYqiEh9BWUENCSQxPhB0kgyh2qjxMWr1TGAShZlqVhRZ8ihG0Xa06anbzaMaqqvqnnvOvd/e51drKdX3nvOdvX/70Pzr1rnnTu1c/Cq+CBAgQIAAAQIVCOxTQQ1KIECAAAECBAjsEhBMnAgECBAgQIBANQKCSTWjUAgBAgQIECAgmDgHCBAgQIAAgWoEBJNqRqEQAgQIECBAQDBxDhAgQIAAAQLVCAgm1YxCIQQIECBAgIBg4hwgQIAAAQIEqhEQTKoZhUIIECBAgAABwcQ5QIAAAQIECFQjIJhUMwqFECBAgAABAoKJc4AAAQIECBCoRkAwqWYUCiFAgAABAgQEE+cAAQIECBAgUI2AYFLNKBRCgAABAgQICCbOAQIECBAgQKAagU6DyfYbrikXvvVV5RmPPahMTU0t/u+A8sTnbC6z37hrFYAflv/1qfeX8888vuy/a7979/2d8udfuGWFfXeUW770/nuOd2j5xd/8s3Lzj3eusL2nCBAgQIAAgZoEOgkmO3fcVD6x+dRyxBGnlU9+42fKeV+6o+zceWv56H+YLtd97A3lpGe8udywl8Cw/cary5nHbyw/feKZ5V3XPbF86O++vbjvzvLj22fLr976oXLqsceXV/zR9eXuZRW3lUtf88byyRsHwee28jcXX1w+83+2L7ulBwkQIECAAIH6BFoPJjvu+GJ5zVOPKc9641x5xgc/U675wG+UnznkIYudbygnnPzUctBUKT+45dby3R0Pxth+40fK85/2vPL+z367HHD4y8vHr7yonHb0w3dtuO/BR5XNb391OXzqhvLuF/+b8nPPeW3Z/IYPletu/9GShQ4rL33r75aTD3/o7uOdeWZ5yqP3X/K8bwkQIECAAIGaBfZrs7jdweKl5eM3/kQ57R1XlXf92k+X+5PPD8rXPv+l8r3F36w89OGHln++7wOPfEu57HXnLO77vVKmfqq85qLXlaN2BZr7t3vIIRvKhn2nyo13by/7PfwXyuvPPbns2cC+5eH/9oxy5Q1n3L9T4O8Gv/5q8jV4hamGL/VPdgrR/Qd6TXqo5fxvWv9gv1p6aOJfU/1NZ1CLf9P6a5vBoJ5hvu7PDcPstcy2g1dKznnpK3cFi0fOnF3e/h+nl4SSUrZ//YryunfMLu65oZx05nPLY/bb8z+6d335snL+n//jrpUfesSzyov+3SOXOYqHCBAgQIAAgcwCLQWT28qV57yqvO1vv1X2OfCXy9vfd2Z51JLgseuVlKf/p/L5764vJ7z8veUdDwgtpewot93w9fJPdw9+0t+/HPXvf/VBwWWwzbe/9Hdl648GV5fsXzYcun6P4JN5SHojQIAAAQJ9EWghmOwoN//lheVV7/viotn+5Ukvfnk5+QkH3eO3+O6aT7+lnPq008uVN/9s+e0//GS58r2nlp9cElp2b3h3Wbj1jvLDwR+mHlGOP+aIZULHQvnK5/7H7m3KuvKExz9qmW3uOax/ECBAgAABAiEF9rxEo0ELO3dcVy787YvLTYNXO6aeUH7t9BPKgYN35bzrknLlR99fPvi1x5SXv/Hy8k+vPGmZQHLvAfcp6w89uPzE4h93hZN7H17yz+1fv7K87cNf3vXIQ5/w6+U/P//RS571LQECBAgQIJBBYORXTL7/1b8uH7v+9t0WO+fKK45+RPnZ576nfO3/7lOefPaW8qO7Pl/e/VsnrxBKBrvuWx71K88rL3jcwxav+rqtXP/1m/ew3bljvlx27kWLvwrasetXRZd87HfKYx/0qsseu/gDAQIECBAgEFBgxFdMflC+fNWnF98ls/vakBNe/1flr3/v+Ea/Ytn34KeU8y67oNz6gleXq37/TeWDR/9+OX0x5Oy446vlbWe8pJz1kb8vjzjuleWPL31zOeFxg7cD+yJAgAABAgSyCYz4isnN5Qtb/mG3yV6vDVkr2e63+n7i+r8sp911dXnpMT+5662C+x1yXPmjHU8vb730c+WGz75TKFkrp+0IECBAgEBAgRFfMWm3412vjrzsN8v1z/7j8r33Pbt4XaRdX6sRIECAAIHaBUZ8xWRJezt/UL5z2+LN0Vb42n7jZ8tn9vY5OTtuKBc899nlrI/eUp507JFCyQqOniJAgAABAlkFRgwmh5bHP/ER99jcUj7+hx8r31z2M3B+WK6/6pxy7FPfU767rOSOctOfXVA2X3PT4rO3lPe+5FfK8875hA/gW9bKgwQIECBAIK/AiMHkYeVpL3l+OXyf3Xdx/dbs68vTTn3Dkk8PHnxK8B+U157y8+UXz/9ueds1l5QTl71wdd+y4bGPL//qnnXKzm+UP33Ts8oj/9kR5bSz3rNkvdUGsfjpwl+4sBz9sP0Wr085tJz0+v9WVvsc49VW9DwBAgQIECAwPoGpxc8EGPGDVe4of3Pui8rT3/ip5e9BMvW4ctrrLijvOPcZq7xl+H+X82eeUs7e8s1lut9QZl52Xnn3W06/5wMBl9lk10MPWGOfE8oV/3BVOe1xB+xth6ofj/45Feqf7OkV3X+g16SHkf9Ka3FsTeofHL6WHqLXP7Bs0kMt/k3rH+xXUw+Deob5GvEVk8GhDi4nvOGj5Wufuqj8+nG7Pwl48OgBj3l2+S9v+XD5+1uvK1f83jNXDCXbb7y6nHHUieUfn3n54of8fb9cf/XF5bwzfmHXDdcGa5VyW5m95Izy5CefXq7e2zUqu7Zb/HTh819djtr1CYEbyolnn11OChpKdrXj/wgQIECAQM8EWnjFZDSxwefonHbCu8svXf6n5RXH3h9sBqvuuGOufPgD7ykXv+nS8sXFm6sNvg4/5YPlqx95SVm8FVv6ryZJf4BSS1JW/2RP0ej+A70mPdRy/jetf7BfLT008a+p/qYzqMW/af21zWBQzzBfEw0mO+64trzsqFPKTad9YsUbsw0+ufisZz5n14cETh10SvmrGy8vv/QvHzJMnyG3jf6Xgvone9pF9x/oNenBf1TaO++a+A+OHn0G0euvbQbDnpEt/Cpn2EPeu/2O8s3/ekW5/MafL2e8+Ekr3i1234OPKpvf/updF9nu/P4d5bY7f3zvIv5JgAABAgQIJBKYYDC5q/z3z31l+QtmlwE+8Mijy/H/Yv8ydeDBZcO6qu4Lt0y1HiJAgAABAgSaCEwwmDykHLJh/eJrfreX79z+/1at/ftbv1D+9julPPlFLyzH9ODXOKuC2IAAAQIECCQUmGAwOaAc/cIXlmMP+p/lvLMu2cuN2XaLD64x2fxbF5ZvPfr0ctGbT3JX2IQnopYIECBAgMBAYILBpJT9H/+C8oE/Obv866+8tjxp5szFD+r7/B43RBu8K+fSt/5GOe6w48pldz+3XPXpC8pRh+S/6NWpSYAAAQIE+iow0Xfl3Iu+/YZryh/8xZ+UK978ofveFjx4bp8Djyln/u4p5eeeeFI548QjJpui7i12jP+MfkW8+sd4sixzqOj+g5aa9OAdFcucDA0fauI/OFT0GUSvv7YZDHv6VRFMhi26L9tH/0tB/ZM9U6P7D/Sa9OA/Ku2dd038B0ePPoPo9dc2g2HPyIn+KmfYYm1PgAABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3cECBAgQCCUgGASalyKJUCAAAECuQUEk9zz1R0BAgQIEAglIJiEGpdiCRAgQIBAbgHBJPd8dUeAAAECBEIJCCahxqVYAgQIECCQW0AwyT1f3REgQIAAgVACgkmocSmWAAECBAjkFhBMcs9XdwQIECBAIJSAYBJqXIolQIAAAQK5BQST3PPVHQECBAgQCCUgmIQal2IJECBAgEBuAcEk93x1R4AAAQIEQgkIJqHGpVgCBAgQIJBbQDDJPV/dESBAgACBUAKCSahxKZYAAQIECOQWEExyz1d3BAgQIEAglIBgEmpciiVAgAABArkFBJPc89UdAQIECBAIJSCYhBqXYgkQIECAQG4BwST3fHVHgAABAgRCCQgmocalWAIECBAgkFtAMMk9X90RIECAAIFQAoJJqHEplgABAgQI5BYQTHLPV3eBBGZmZsrU1NRe/zc7OxuoG6X2WWDz5s0TbX/pv0tdFrLSv6+D53w1ExBMmrnZiwABAgQIEOhAYGrn4lcH6/Z2SSm5t6PXOAECBFIKjDsmeMWkg9NoMMS2/3fttdeuWOm5557b+jHb7sF6K58XmzZtWnHGg3Ogb4aD83qlr4jnfYY51z6X1epr69+llc7NwXOr/fs6zP6T+m/AajV28bxg0oWqNQkQIECAAIFGAoJJIzY7ESBAgAABAl0ICCZdqFqTAAECiQWmp6cTd6e1SQsIJpOegOMTIEAgmMD69euDVazcSAKCSaRprVDr3NzcCs96igABAgRqEzjssMNaKynTfY4Ek9ZOi8kutLCwMNkCHJ0AAQIEhhLYuHHjUNv3ZWPBpC+T1ieBgAL+4g44NCUTGFFAMBkR0O4ECHQnIJh0Z9vnldv61fe6dev6zNhZ74JJZ7QWJkCAQD8Far/eoa1ffXt3Ujfnt2DSjatVCRAgQIAAgQYCgkkDNLsQIECAAIGuBWp/5amr/gWTrmStS4AAAQIECAwtIJgMTWYHAgRqEejrT5S1+KuDQBcCgkkXqtYk0EDAhXQN0OxCoGKBtt79U3GLnZQmmHTCalECwwu4zffwZvYgULNAW+/+qbnHLmoTTLpQtSYBAgQIECDQSEAwacRmJwIECBAgQKALAcGkC1VrEiBAgAABAo0EBJNGbHYiMH4Bv68ev7kjEiAwfgHBZPzmjkigkYAr/Bux2YkAgWACgkmwgSmXAAECBAhkFhBMMk9XbwQIVCfgbeHVjURBlQkIJpUNRDkECOQWcCO93PPV3egCgsnohlYgQIAAAQIEWhIQTFqCtAwBAgQIECAwuoBgMrqhFQgQIECAAIGWBASTliAtQ4AAAQIECIwuIJiMbmgFAgQItCYwPz/f2loWIhBRQDAJMrWNGzcGqVSZBAiMIiCYjKKXd98+vZtLMAlyHgsmQQalTAIECHQg0Kf73wgmHZxAliRAgAABAgSaCQgmzdzsRYAAAQIECHQgIJh0gGpJAgQIZBbo0/UOmedYa2+CSa2TURcBAgQqFejT9Q6VjuBBZS0sLDzosagPCCZRJ/eAurds2fKAR/yRAAECBGoWaPOVp61bt9bc6lC1CSZDcdmYAAECBAi0I+CVp+UdBZPlXTxKgEAFAm3+RFlBO0ogQGANAoLJGpBsQoDAZAT8RDkZ91GPmul6h5Us3F9qJZ3mzwkmze3sSYAAAQLLCGS63mGZ9u57SDC5j6LVbwSTVjktRoAAAQIECIwiIJiMomdfAgQIECDQkcDs7GxHK9e9rGBS93xUR4AAAQIEeiUgmPRq3JolkEvA/XtyzVM3BAYCgonzgEAlAjMzM5VUogwCsQVquSi1r7+KGfXsEUxGFbQ/AQIECFQlUEswqQolUDGCSaBhKZUAAQIECGQXEEyyT1h/BAgQIEAgkIBgEmhYSiVAgAABAtkFBJPsE9ZfGoH5+fk0vWiEAAECexMQTPYm43EClQkIJpUNRDkECHQiIJh0wmpRAgQIECBAoImAYNJEzT4ECBBoKOATkxvC2a03AoJJb0atUQIEahCYnp6uoYxe1zA3N9fr/mtvXjCpfULqI0CAAIFWBRYWFlpdz2LtCggm7XpajQABAgQIEBhBQDAZAc+uBAgQIECAQLsCgkm7nlYjQIAAAQIERhAQTEbAsysBAgTaFnBhZtui1osmIJgEmtiRRx4ZqFqlEiDQRMCFmU3U+rHPpk2betGoYBJozO5/EGhYSiVAgACBRgKCSSM2OxEgQIAAAQJdCAgmXahakwABAgQIEGgkIJg0YrMTAQIE+i3Ql+sd+j3lyXQvmEzG3VEJECBAgECrAlk+gVwwafW0mOxis7Ozky3A0QkQIEBgzQIzMzNr3nYtGwoma1GyDQECBAgQIEBgCAGvmAyBZVMCBMYv4P494zd3RAKTFBBMJqnv2AQIrCrg/j2rElW5QR9uFDc9PV2lffSiBJPoE1Q/AQIEKhTow631heZuTjzBpBtXqxIgQIAAgZEE+vCq03JAgslyKh4jQIAAAQITFujDq07LEQsmy6l4jACBMAJ9/akyzIAUSmBIAcFkSDCbE+hKwO+rm8n29afKZlr2IlC/gGBS/4xU2BMBV/j3ZNDa7I2Am142G7Vg0szNXgQIECBAgEAHAoJJB6iWJECAAAECBJoJCCbN3OxFgAABAgQIdCAgmHSAakkCBAgQIECgmYBg0szNXgTGLpDlk0PHDueABAiEEhBMQo1LsX0W2LZtW5/b1zsBAj0REEx6MmhtEiBAgACBCAKCSYQpqZEAgTQCGzduTNOLRgh0ISCYdKFqTQIECOxFQDDZC4yHCdwjIJg4FQgQIECAAIFqBASTakahEAIECBAgQEAwcQ4QIECAAAEC1QgIJtWMQiEECBAgQICAYOIcIECAQEUCW7ZsqagapdQksH79+prK6awWwaQz2vYXnpmZaX9RKxIgQCCZwPT0dLKOdreTta8HDksweaCIPxMgQIBAaIG+vLIQekgrFC+YrIDjKQIECBAgQGC8AoLJeL0djQABAgQIEFhBQDBZAcdTBAgQILC8gGvelnfx6OgCgsnohtWssLCwUE0tCiFAgACB8QrMz8+P94AdHU0w6Qh2EsvOzc1N4rCOSYAAAQINBNp+1UkwaTAEuxAgQIAAAQIEVhLwislKOp4jQGDiAm3/VDnxhhRAgMCKAoLJijyeJECAAIEmAjX/WqGtu+v25YZnTeY/yj6CySh69iVAgACBZQVqDibLFtzgQTdya4C2hl0EkzUg2YQAAQIECIxboA/hbjlTwWQ5FY8RIECAAIEJC2zbtm3CFUzm8ILJZNwdlQCBlgT6+lNlS3yWIVCdgGBS3UgU1GeBdevW9bn9Rr0LJo3Y7DQGATe9bIYsmDRzsxeBTgRc5d8Jq0UJTERg69atEzlu9IMKJtEnqH4CBAgQIJBIQDBJNEytECBAgACB6AKCSfQJqp8AAQIECCQSEEwSDVMrBAgQIEAguoBgEn2C6u+VgE+Q7tW4NUuglwKCSS/HrumoAt5+GHVy6iZAYK0CgslapWxHgAABAgQIdC4gmHRO7AAECBDYU+DII4/c8wF/IkDgPgHB5D4K3xAgQGA8Aj6VdjzOjhJTQDCJOTdVEyBAgACBlAKCScqxaooAAQIECMQUEExizk3VBAgQIEAgpYBgknKsmiJAgAABAjEFBJOYc1M1AQKJBWZnZxN3p7WmAn25aFowaXqGTGC/mZmZCRzVIQkQIECgBoHp6ekayui8BsGkc2IHIECAAAECBNYqIJisVcp2BAgQIECAQOcCgknnxA5AgACBfAJ9ud4h3+Tq70gwqX9GKiRAgEB1An253qE6+B4UJJgkGvL8/HyibrRCgACB/ALr1q1rrcm5ubnW1prkQoLJJPVbPrZg0jKo5QgQINCxQJuvPC0sLHRc7XiWF0zG4+woBAg0FHAtQ0M4uxEIKiCYBB2csgn0RaDNnyj7YqZPApEFBJPI01M7AQIEKhXIcr3DarybNm1abRPPDykgmAwJZnMCBAgQWF0gy/UOq3dqi7YFBJO2Ra1HgAABAgRaEujjmxoEk5ZOHssQIECAAIG2BQSTtkWtR4AAgY4F+vgXd8eklicwUQGvmEyU38EJ7CmwcePGPR/wp1UFBJNViWwwQQHX2gyPL5gMb2YPAp0JCCad0Vq4ZwK1vFumL+9OavP0Ekza1LQWAQIECBAgMJKAYDISn50JECBAgACBNgUEkzY1rUWAAAECBAiMJCCYjMRnZwIECBAgQKBNAcGkTU1rEehYwIV0HQNbngCBiQsIJhMfgQIIrF3AWw/XbmVLAgRiCggmMeemagIECBAgkFJAMEk5Vk0RIFCzwPT0dM3l9aI2rz7WO2bBpN7ZqIwAgaQC69evT9pZnLZcr1XvrASTemejMgIECBAg0DsBwaR3I9cwAQIECBCoV0AwqXc2KiNAgAABAr0TEEx6N3INEyBQu4ALM2ufkPq6FBBMutRteW0XzLUMajkClQq4MLPSwUy4rL58+rhgMuETbZjDe4vhMFq2JUCAQC4BwSTXPHVDgAABAgQIBBDwikmAISmRAAECBAj0RUAw6cuk9UmAAIEWBfrya4UWySy1RgHBZI1QNiNAgACB+wUEk/stfNeugGDSrudEV5ufn5/o8R2cAAECBIYTaPPdllnezSWYDHcOVb31tm3bqq5PcQQIECCwp0Cb77a8884791w86J8Ek6CDUzaBvgi0+RNlX8z0SSCygGASeXpqJ9ADgTZ/ouwBlxbHLCA4tw8umLRvakUCBAj0XiDL9Q6rDVJwXk1o+OcFk+HN7EGAAAECqwhkud5hlTY93YGAYNIBqiUJECBAgEAbAn155WmplWCyVMP3BAgQIECgIoE+ftK0YFLRCagUAgSGF+jjT5TDK9mDQBwBwSTOrFTaAwEX0g0/ZNcyDG9mj/EJuPHl8NaCyfBm9iDQmYC3HnZGa2ECExEQTIZnF0yGN7MHAQIECBAg0JGAYNIRrGUJECBAgACB4QUEk+HN7EGAAAECBAh0JCCYdARrWQIECBAgQGB4AcFkeDN7EJiYwOzs7MSO7cAECBAYh4BgMg5lxyBAgAABAgTWJCCYrInJRgQIECBAgMA4BASTcSg7BgECBJYIzMzMLPmTbwkQWCogmCzV8D0BAgQIECAwUQHBZKL8Dk6AAAECBAgsFRBMlmr4ngABAgQIEJiogGAyUX4HJ0CAAAECBJYKCCZLNXxPgACBCgQWFhYqqEIJBCYjIJhMxr3xUdetW9d4XzsSIBBDYG5uLkahFVeZ9ZO6DzvssIrV2ylNMGnHcWyrTE9Pj+1YDkSAAIGoAln/rty4cWPUkay5bsFkzVQ2JECAAAECBLoWEEy6FrY+AQIECBAgsGYBwWTNVDYkQIAAgaUCfbjeYWm/vh+PgGAyHmdHIUCAQDqBPlzvkG5oARoSTAIMaZgSXc0/jJZtCRAgMFmBtsPd7OzsZBtq4eiCSQuINS3h/gc1TUMtBAgQWFmg7WCy8tFiPCuYxJiTKgn0WsC1DL0ev+Z7JiCY9Gzg2iUQUcBPlRGnVnfN8/PzrRSY9UZureA0XEQwaQhnNwIECBBYWaDm6x3aCiZZb+S28mS7fVYw6dbX6gQIECBAgMAQAoLJEFg2JUCAAAEC4xSo+VWnrhwEk65krUuAAAECBAgMLSCYDE1mBwIEahPo40+Vtc1APQTaEhBM2pK0DoEWBFxI1wKiJQhUJOCml8MPQzAZ3sweBDoT8NbDzmgtTGAiAm56OTy7YDK8mT0IECBAgACBjgQEk45gLUuAAAECBAgMLyCYDG9mDwIECBAgQKAjAcGkI1jLEuhCwO+ru1C1JgECNQkIJjVNQy0EVhHYunXrKlt4mgABArEFBJPY81M9AQIECBBIJSCYpBqnZggQiCDgbeERpqTGSQkIJpOSd1wCBHor4EZ6vR29xtcgIJisAckmBAgQIECAwHgEBJPxODsKAQIECBAgsAYBwWQNSDYhQIAAAQIExiMgmIzH2VEIECBAgACBNQgIJmtAsgkBAgTGKTA/Pz/OwzkWgaoEBJOqxrF6MRs3blx9I1sQIBBaYNu2baHrV3x3An14R5dg0t3508nKgkknrBYlQIBACIE+3ANHMAlxKiqSAAECBAj0Q0Aw6cecdUmAAAECBEIICCYhxqRIAgQI1CfQh+sd6lPPX5Fgkn/GOiRAgEAnAn243qETuA4XXVhY6HD18SwtmIzHeWxHmZ2dHduxHIgAAQIERhNo+1Wnubm50QqqYG/BpIIhKIEAAQIE+ingVacHz10webCJRwgQqEyg7Z8qK2tPOQQILBEQTJZg+JYAgToF/FRZ51xWqyrD9Q6r9ejeUqsJDf+8YDK8mT0IECBAYA0CGa53WK1NwWQ1oeGfF0yGN7MHAQIECBAg0JGAYNIRrGUJECBAgMCoAlu2bBl1iXD7CybhRqZgAgQIECCQV0AwyTtbnRHojYD79/Rm1BrtgYBg0oMhazGWwKZNm2IVrFoCFQrU8k6uPlwA3Pb4BZO2Ra1HgAABAhMXqOXeN3feeefELaIVsF+0gvte7+mnn15mZmb2yuCta3ul8QQBAgQIBBAQTAIMaWmJg+AhfCwV8T0BAgQIZBIQTDJNUy8pBN75znfu6qOWl6JrQL33lcKVXi2soc5harj22mvL4DqIyHOueS4D1507dw4zksbbDmbph8bGfA/aUTB5EIkHCExWIPJ/qLqSy/iXfoaQVfNcxnnxa4ZZdvXvbpN1pxYT5XgiZZPqAu4zNTU1tpQekEfJBAgQIBBIYBL/TfOunEAniFIJECBAgEB2AcEk+4T1R4AAAQIEAgkIJoGGpVQCBAgQIJBdQDDJPmH9ESBAgACBQAKCSaBhKZUAAQIECGQXEEyyT1h/BAgQIEAgkIBgEmhYSiVAgAABAtkFBJPsE9YfAQIECBAIJCCYBBqWUgkQIECAQHYBwST7hPVHgAABAgQCCQgmgYalVAIECBAgkF1AMMk+Yf0RIECAAIFAAoJJoGEplQABAgQIZBcQTLJPWH8ECBAgQCCQgGASaFhKJUCAAAEC2QUEk+wT1h8BAgQIEAgkIJgEGpZSCRAgQIBAdgHBJPuE9UeAAAECBAIJCCaBhqVUAgQIECCQXUAwyT5h/REgQIAAgUACgkmgYSmVAAECBAhkFxBMsk9YfwQIECBAIJCAYBJoWEolQIAAAQLZBfbL3uAk+puamprEYR2TAAECBAiEFxBMWh7hzp07W17RcgQIECBAoD8CfpXTn1nrlAABAgQIVC8gmFQ/IgUSIECAAIH+CAgm/Zm1TgkQIECAQPUCgkn1I1IgAQIECBDoj4Bg0p9Z65QAAQIECFQvIJhUPyIFEiBAgACB/ggIJv2ZtU4JECBAgED1AoJJ9SNSIAECBAgQ6I+AYNKfWeuUAAECBAhULyCYVD8iBRIgQIAAgf4ICCb9mbVOCRAgQIBA9QKCSfUjUiABAgQIEOiPgGDSn1nrlAABAgQIVC8gmFQ/IgUSIECAAIH+CAgm/Zm1TgkQIECAQPUCgkn1I1IgAQIECBDoj4Bg0p9Z65QAAQIECFQvIJhUPyIFEiBAgACB/gj8f/DCpcNTZ5m0AAAAAElFTkSuQmCC" alt></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 26">
<div class="layoutArea">
<div class="column">
<p><span style="font-size: 10.000000pt; font-family: 'Arial';">This part of syllabus does not appear to be well understood. Some candidates calculated the wavelength but many used the formula from the data booklet without explanation. Only a few analysed the situation well. Even the well prepared candidates had a problem with the radian angle unit. The majority of candidates found the change in shape of one of the plates very difficult. Only a few candidates realized that the number of fringes must not change. </span></p>
</div>
</div>
</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 26">
<div class="layoutArea">
<div class="column">
<p><span style="font-size: 10.000000pt; font-family: 'Arial';">This part of syllabus does not appear to be well understood. Some candidates calculated the wavelength but many used the formula from the data booklet without explanation. Only a few analysed the situation well. Even the well prepared candidates had a problem with the radian angle unit. The majority of candidates found the change in shape of one of the plates very difficult. Only a few candidates realized that the number of fringes must not change. </span></p>
</div>
</div>
</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>