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<h2>SL Paper 3</h2><div class="specification">
<p><span style="background-color: #ffffff;">The refractive index <span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span></span> of a material is the ratio of the speed of light in a vacuum <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>, to the speed of light in the material <span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = \frac{c}{v}">
<mi>n</mi>
<mo>=</mo>
<mfrac>
<mi>c</mi>
<mi>v</mi>
</mfrac>
</math></span>.<br></span></p>
<p><span style="background-color: #ffffff;">The speed of light in a vacuum <span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span></span> is 2.99792 × 10<sup>8</sup> m s<sup>-1</sup>. The following data are available for the refractive indices of the fibre core for two wavelengths of light:</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Outline the differences between step-index and graded-index optic fibres.</span></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><span style="background-color:#ffffff;">Determine the difference between the speed of light corresponding to these two wavelengths in the core glass.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">An input signal to the fibre consists of wavelengths that range from 1299 nm to 1301 nm. The diagram shows the variation of intensity with time of the input signal.</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Sketch, on the axes, the variation of signal intensity with time after the signal has travelled a long distance along the fibre.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain the shape of the signal you sketched in (b)(ii).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">A signal consists of a series of pulses. Outline how the length of the fibre optic cable limits the time between transmission of pulses in a practical system.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">biv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">refractive index of step index fibre is constant ✔<br></span></p>
<p><span style="background-color:#ffffff;">refractive index of graded index fibre decreases with distance from axis/centre ✔<br></span></p>
<p><span style="background-color:#ffffff;">graded index fibres have less dispersion ✔<br></span></p>
<p><span style="background-color:#ffffff;">step index fibre: path of rays is in a zig-zag manner ✔<br></span></p>
<p><span style="background-color:#ffffff;">graded index fibre: path of rays is in curved path ✔</span><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><br></span></span></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">For MP2 do not accept vague statements such as “index increases/varies with distance from centre”.</span></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \frac{c}{n} = {v_{1299}} = \frac{{2.99792 \times {{10}^8}}}{{1.45061}} = 2.06666 \times {10^8}">
<mi>v</mi>
<mo>=</mo>
<mfrac>
<mi>c</mi>
<mi>n</mi>
</mfrac>
<mo>=</mo>
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mn>1299</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.99792</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.45061</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2.06666</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>8</mn>
</msup>
</mrow>
</math></span> «ms<sup>–1</sup>» <em><strong>AND</strong></em></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{1301}} = \frac{{2.99792 \times 10{}^8}}{{1.45059}} = 2.06669 \times {10^8}">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mn>1301</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.99792</mn>
<mo>×</mo>
<mn>10</mn>
<msup>
<mrow>
</mrow>
<mn>8</mn>
</msup>
</mrow>
<mrow>
<mn>1.45059</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2.06669</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>8</mn>
</msup>
</mrow>
</math></span>«ms<sup>–1</sup>»</span></span></p>
<p><em><strong>OR</strong></em></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta v = \left( {\frac{1}{{1.45059}} - \frac{1}{{1.45061}}} \right) \times 2.99792 \times {10^8}">
<mi mathvariant="normal">Δ</mi>
<mi>v</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1.45059</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1.45061</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>2.99792</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>8</mn>
</msup>
</mrow>
</math></span> ✔</span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta v = 2.85 \times {10^3}">
<mi mathvariant="normal">Δ</mi>
<mi>v</mi>
<mo>=</mo>
<mn>2.85</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>3</mn>
</msup>
</mrow>
</math></span> <em><strong>OR</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 \times {10^3}">
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>3</mn>
</msup>
</mrow>
</math></span>«ms<sup><span style="font-size:small;">–1</span></sup>»✔</span></span></p>
<p> </p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">pulse wider ✔<br></span></p>
<p><span style="background-color:#ffffff;">pulse area smaller ✔</span></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">For MP2 do not accept lower amplitude unless pulse area is also smaller.</span></span></em></p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">reference to dispersion<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">reference to time/speed/path difference ✔<br></span></p>
<p><span style="background-color:#ffffff;">reference to power loss/energy loss/scattering/attenuation ✔</span></p>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">longer cables give wider pulses ✔<br></span></p>
<p><span style="background-color:#ffffff;">which overlap/interfere if <em>T</em> too small/<em>f</em> too high ✔</span></p>
<p><em><span style="background-color:#ffffff;">OWTTE</span></em></p>
<div class="question_part_label">biv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The differences between step index fibres and graded index fibres seem well-known.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The calculation of the difference in the speed of light for two different wavelengths was well answered. Candidates often rounded answers to a small number of significant figures when finding the individual speeds.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates correctly drew a wider pulse with smaller area.</p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Correct answers mentioning dispersion and attenuation were common but few candidates were able to relate those phenomena to the shape of the pulse drawn.</p>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates did not mention the fact that if the time between pulses was too small then the pulses would overlap for longer fibres.</p>
<div class="question_part_label">biv.</div>
</div>
<br><hr><br>