{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 4: DIFFRACTION"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.1: Diffraction_at_a_single_slit.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.1 : Page-91 (2010)\n",
"D = 50;    // Distance between source and the screen, cm\n",
"lambda = 6563e-008;    // Wavelength of light of parallel rays, m\n",
"d = 0.385e-01;        // Width of the slit, cm\n",
"n = 1;    // Order of diffraction for first minimum\n",
"// As sin(theta1) = n*lambda/d = x1/D, solving for x1\n",
"x1 = n*lambda*D/d;    // Distance from the centre of the principal maximum to the first minimum, cm\n",
"printf('\nThe Distance from the centre of the principal maximum to the first minimum = %4.2f mm', x1/1e-001);\n",
"n = 5;    // Order of diffraction for fifth minimum\n",
"x2 = n*lambda*D/d;    // Distance from the centre of the principal maximum to the fifth minimum, cm\n",
"printf('\nThe Distance from the centre of the principal maximum to the fifth minimum = %4.2f mm', x2/1e-001);\n",
"\n",
"// Result \n",
"// The Distance from the centre of the principal maximum to the first minimum = 0.85 mm\n",
"// The Distance from the centre of the principal maximum to the fifth minimum = 4.26 mm"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.2: Diffraction_at_a_circular_aperture.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.2 : Page-91 (2010)\n",
"D = 0.04;    // Diameter of circular aperture, cm\n",
"f = 20;    // Focal length of convex lens, cm\n",
"lambda = 6000e-008;    // Wavelength of light used, m\n",
"// We have sin(theta) = 1.22*lambda/D = theta, for small theta, such that\n",
"// For first dark ring\n",
"theta = 1.22*lambda/D;    // The half angular width at central maximum, rad\n",
"r1 = theta*f;    // The half width of central maximum for first dark ring, cm\n",
"// We have sin(theta) = 5.136*lambda/(%pi*D) = theta, for small theta, such that\n",
"// For second dark ring\n",
"theta = 5.136*lambda/(%pi*D);    // The half angular width at central maximum, rad\n",
"r2 = theta*f;    // The half width of central maximum for second dark ring, cm\n",
"printf('\nThe radius of first dark ring = %4.2e cm', r1);\n",
"printf('\nThe radius of second dark ring = %4.1e cm', r2);\n",
"\n",
"// Result \n",
"// The radius of first dark ring = 3.66e-002 cm\n",
"// The radius of second dark ring = 4.90e-002 cm"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.3: Second_order_maximum_for_diffraction_grating.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.3 : Page-91 (2010)\n",
"n = 2;    // Order of diffraction\n",
"lambda = 650e-009;    // Wavelength of light used, m\n",
"d = 1.2e-05;    // Distance between two consecutive slits of grating, m\n",
"// We have sin(theta) = n*N*lambda = n*lambda/d, solving for theta\n",
"theta = asind(n*lambda/d);    // Angle at which the 650 nm light produces a second order maximum, degrees\n",
"printf('\nThe angle at which the 650 nm light produces a second order maximum = %4.2f degrees', theta);\n",
"\n",
"// Result \n",
"// The angle at which the 650 nm light produces a second order maximum = 6.22 degrees "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.4: The_highest_spectral_order_with_diffraction_grating.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.4 : Page-92 (2010)\n",
"lambda = 650e-009;    // Wavelength of light used, m\n",
"N = 6000e+02;    // Number of lines per m on grating, per m\n",
"theta = 90;    // Angle at which the highest spectral order is obtained, degrees\n",
"// We have sin(theta) = n*N*lambda, solving for n\n",
"n = sind(theta)/(N*lambda);    // The highest order of spectra with diffraction grating\n",
"printf('\nThe highest order of spectra obtained with diffraction grating = %1d', n);\n",
"\n",
"// Result \n",
"// The highest order of spectra obtained with diffraction grating = 2"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.5: Overlapping_spectra_with_diffraction_grating.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.5 : Page-92 (2010)\n",
"N = 4000e+02;    // Number of lines per m on grating, per m\n",
"// For Blue Line\n",
"lambda = 450e-009;    // Wavelength of blue light, m\n",
"n = 3;    // Order of diffraction spectrum\n",
"// We have sin(theta) = n*N*lambda, solving for sin(theta)\n",
"sin_theta_3 = n*N*lambda;    // Sine of angle at third order diffraction \n",
"// For Red Line\n",
"lambda = 700e-009;    // Wavelength of blue light, m\n",
"n = 2;    // Order of diffraction spectrum\n",
"// We have sin(theta) = n*N*lambda, solving for sin(theta)\n",
"sin_theta_2 = n*N*lambda;    // Sine of angle at second order diffraction\n",
"// Check for overlapping\n",
"if abs(sin_theta_3 - sin_theta_2) < 0.05 then\n",
"    printf('\nThe two orders overlap.');\n",
"else\n",
"    printf('\nThe two orders do not overlap.');\n",
"end\n",
"\n",
"// Result \n",
"// The two orders overlap. "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.6: Width_of_first_order_spectrum.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.6 : Page-93 (2010)\n",
"n = 1;    // Order of diffraction spectrum\n",
"N = 6000e+02;    // Number of lines per m on diffraction grating, per m\n",
"D = 2;    // Distance of screen from the source, m\n",
"lambda1 = 400e-009;    // Wavelength of blue light, m\n",
"// We have sin(theta1) = n*N*lambda, solving for theta1\n",
"theta1 = asind(n*N*lambda1);    // Angle at first order diffraction for Blue light, degrees\n",
"lambda2 = 750e-009;    // Wavelength of blue light, m\n",
"// We have sin(theta2) = n*N*lambda, solving for theta2\n",
"theta2 = asind(n*N*lambda2);    // Angle at first order diffraction for Red light, degrees\n",
"x1 = D*tand(theta1);    // Half width position at central maximum for blue color, m\n",
"x2 = D*tand(theta2);    // Half width position at central maximum for red color, m\n",
"\n",
"printf('\nThe width of first order spectrum on the screen = %4.1f cm', (x2 - x1)/1e-02);\n",
"\n",
"// Result \n",
"// The width of first order spectrum on the screen = 51.3 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.7: Resolution_of_wavelengths_for_grating.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.7 : Page-93 (2010)\n",
"w = 5;    // Width of the grating, cm\n",
"N = 320;    // Number of lines per cm on grating, per cm\n",
"N0 = w*N;    // Total number of lines on the grating\n",
"lambda = 640;    // Wavelength of light, nm\n",
"n = 2;    // Order of diffraction\n",
"d_lambda = lambda/(n*N0);    // Separation between wavelengths which the gratign can just resolve, nm\n",
"printf('\nThe separation between wavelengths which the grating can just resolve = %3.1f nm', d_lambda);\n",
"\n",
"// Result \n",
"// The separation between wavelengths which the grating can just resolve = 0.2 nm"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.8: Angular_separation_to_satisfy_Rayleigh_criterion.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.8 : Page-93 (2010)\n",
"lambda = 550e-09;    // Wavelength of light, m\n",
"D = 3.2e-02;    // Diameter of circular lens, m\n",
"f = 24e-02;    // Focal length of the lens, m    \n",
"theta_min = 1.22*lambda/D;    // Minimum angle of resolution provided by the lens, rad\n",
"// As delta_x/f = theta_min, solving for delta_x\n",
"delta_x = theta_min*f;    // Separation of the centres of the images in the focal plane of lens, m\n",
"printf('\nThe separation of the centres of the images in the focal plane of lens = %1d micro-metre', delta_x/1e-06);\n",
"\n",
"// Result \n",
"// The separation of the centres of the images in the focal plane of lens = 5 micro-metre"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.9: Linear_separation_between_two_points.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex4.9 : Page-94 (2010)\n",
"lambda = 550e-09;    // Wavelength of light, m\n",
"D = 20e-02;    // Diameter of objective of telescope, m\n",
"d = 6e+003;    // Distance of two points from the objective of telescope, m\n",
"theta = 1.22*lambda/D;    // Angular separation between two points, rad\n",
"x = theta*d;    // Linear separation between two points, m\n",
"printf('\nThe linear separation between two points = %5.2f mm', x/1e-03);\n",
"\n",
"// Result \n",
"// The linear separation between two points = 20.13 mm"
   ]
   }
],
"metadata": {
		  "kernelspec": {
		   "display_name": "Scilab",
		   "language": "scilab",
		   "name": "scilab"
		  },
		  "language_info": {
		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
			}
		   ],
		   "mimetype": "text/x-octave",
		   "name": "scilab",
		   "version": "0.7.1"
		  }
		 },
		 "nbformat": 4,
		 "nbformat_minor": 0
}