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Adding Wolfe Chapter 27, Wave Optics
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‎Contrib/Keele/College_Physics_Wolfe/27.Wave_Optics/27-01.Interference/NU_U17-27-01-001.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Optics)
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## DBchapter(Wave Optics)
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## DBsection(The Wave Aspect of Light Interference)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('27.1')
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## Problem1('1')
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## MO(1)
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## KEYWORDS('wavelength')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'MathObjects.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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($medium, $index) = @{ list_random(
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[water => 1.333],
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[ethanol => 1.361],
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[fluorite => 1.434],
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[glycerine => 1.473],
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[benzene => 1.501],
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['crown glass' => 1.52],
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['sodium chloride' => 1.544],
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['flint glass' => 1.66],
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[zircon => 1.923],
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[diamond => 2.419],
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) };
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$decrease = Real( 1/$index );
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ANS( $decrease->cmp );
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BEGIN_TEXT
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When light passes from air to $medium,
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its wavelength decreases by how much of its original value?
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The index of refraction for $medium is \( \eta = $index\)
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$PAR
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\(\lambda_n = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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What is the index of refraction for $medium?
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle \lambda_{\textrm{$medium}} = \frac{1}{\eta} \lambda_{air}
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= \frac{1}{$index} \lambda_{air}
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= $decrease \ \lambda_{air}
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\)
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END_SOLUTION
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/27.Wave_Optics/27-01.Interference/NU_U17-27-01-002.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Optics)
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## DBchapter(Wave Optics)
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## DBsection(The Wave Aspect of Light Interference)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('27.1')
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## Problem1('2')
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## MO(1)
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## KEYWORDS('wavelength','refraction')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$medium = list_random(
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[fluorite => 1.434],
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['crown glass' => 1.52],
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['flint glass' => 1.66],
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[zircon => 1.923],
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[diamond => 2.419],
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);
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($name, $index) = ($medium->[0], Real($medium->[1]));
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$blue = NumberWithUnits( random(380, 400, 10), 'nm');
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$red = NumberWithUnits( random(700, 760, 10), 'nm');
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$blue_new = $blue / $index;
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$red_new = $red / $index;
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ANS( $blue_new->cmp );
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ANS( $red_new->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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Find the range of visible wavelengths of light in $name.
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\{ ucfirst $name \} has an index of refraction equal to $index
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and visible light has a wavelength range from \($blue\) to \($red\).
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$PAR
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\{ans_rule(15)\} to \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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How would you expect wavelength to change, if at all, when entering a substance with a higher index of refraction from a lower index?
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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The wavelength of blue light in $name is \( \displaystyle \lambda = \frac{$blue}{$index} = $blue_new \).
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$PAR
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The wavelength of red light in $name is \( \displaystyle \lambda = \frac{$red}{$index} = $red_new \).
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END_SOLUTION
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COMMENT('Uses NumberWithUnits');
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/27.Wave_Optics/27-01.Interference/NU_U17-27-01-003.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Optics)
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## DBchapter(Wave Optics)
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## DBsection(The Wave Aspect of Light Interference)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('27.1')
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## Problem1('3')
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## MO(1)
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## KEYWORDS('refraction')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$a = random(0.2,0.9,0.001);
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$index = Real(1 / $a);
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ANS( $index->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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What is the index of refraction of a material for which the wavelength of light is \($a\) times its value in a vacuum?
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$PAR
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\( \eta = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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How would you find wavelength when a substance is entering a substance of higher refractive index.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle \eta = \frac{1}{$a} = $index \)
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END_SOLUTION
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/27.Wave_Optics/27-01.Interference/NU_U17-27-01-004.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Optics)
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## DBchapter(Wave Optics)
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## DBsection(The Wave Aspect of Light Interference)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('27.1')
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## Problem1('4')
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## MO(1)
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## KEYWORDS('wavelength','refraction')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$lambda_solid = NumberWithUnits( random(380, 500, 0.1), 'nm');
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$lambda_air = NumberWithUnits( random(501, 760, 0.1), 'nm');
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$index = Real($lambda_air->value / $lambda_solid->value);
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ANS( $index->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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Analysis of an interference effect in a clear solid shows that
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the wavelength of light in the solid is \($lambda_solid\).
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Knowing this light comes from a He-Ne laser and has a wavelength of \($lambda_air\) in air,
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find the index of refraction.
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$PAR
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\( \eta = \) \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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How would you calculate wavelength as light passes into a different refractive index?
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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\( \displaystyle \eta = \frac{\lambda_{air}}{\lambda_{solid}}
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= \frac{$lambda_air}{$lambda_solid}
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= $index
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\)
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END_SOLUTION
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ENDDOCUMENT();

‎Contrib/Keele/College_Physics_Wolfe/27.Wave_Optics/27-01.Interference/NU_U17-27-01-005.pg‎

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##DESCRIPTION
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# originally written by Brandon Lostracco and Sara Hesse, Brock University, 2018
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# cleaned up, added solution and re-written to use NumberWithUnits
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##ENDDESCRIPTION
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## DBsubject(Optics)
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## DBchapter(Wave Optics)
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## DBsection(The Wave Aspect of Light Interference)
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## Date(December 2021)
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## Institution(Keele University)
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## Author(Boyd Duffee)
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## TitleText1('College Physics')
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## AuthorText1('Wolfe et. al')
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## EditionText1('2015')
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## Section1('27.1')
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## Problem1('5')
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## MO(1)
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## KEYWORDS('refraction')
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DOCUMENT();
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loadMacros(
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'PGstandard.pl',
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'parserNumberWithUnits.pl',
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);
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TEXT(beginproblem());
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Context("Numeric")->flags->set( tolerance => 0.005 );
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$showPartialCorrectAnswers = 1;
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$showHint = 3;
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$liquid = list_random(
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{name => 'water', index => 1.333},
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{name => 'ethanol', index => 1.361},
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{name => 'glycerine', index => 1.473},
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{name => 'benzene', index => 1.501},
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);
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$solid = list_random(
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{name => 'crown glass', index => 1.52},
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{name => 'sodium chloride', index => 1.544},
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{name => 'flint glass', index => 1.66},
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{name => 'zircon', index => 1.923},
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{name => 'diamond', index => 2.419},
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);
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$ratio = Real($liquid->{index} / $solid->{index});
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ANS( $ratio->cmp );
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Context()->texStrings;
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BEGIN_TEXT
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What is the ratio of thicknesses of $solid->{name} and $liquid->{name} would contain
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the same number of wavelengths of light?
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\{ ucfirst $solid->{name} \} has an index of refraction equal to \($solid->{index}\)
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and $liquid->{name} has an index of refraction equal to \($liquid->{index}\).
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$PAR
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ratio = \{ans_rule(15)\}
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END_TEXT
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BEGIN_HINT
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Is there a formula regarding index of refraction which may be used to form a ratio?
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Keep in mind, when creating ratios you want to be able to divide out unknowns.
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END_HINT
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BEGIN_SOLUTION
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$PAR $BBOLD SOLUTION $EBOLD $PAR
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ratio \( \displaystyle = \frac{\lambda_{ $liquid->{name} }}{\lambda_{ $solid->{name} }}
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= \frac{ $liquid->{index} }{ $solid->{index} }
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= $ratio
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\)
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END_SOLUTION
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ENDDOCUMENT();

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