{"id":56965,"date":"2024-04-16T00:53:52","date_gmt":"2024-04-16T00:53:52","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=56965"},"modified":"2024-04-16T00:53:52","modified_gmt":"2024-04-16T00:53:52","slug":"the-dispersion-due-to-material-waveguide-and-profile-are-2-8nm-1km-1-20-1nm-1km-1-and-23-2nm-1km-1-respectively-find-the-total-first-order-dispersion","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-dispersion-due-to-material-waveguide-and-profile-are-2-8nm-1km-1-20-1nm-1km-1-and-23-2nm-1km-1-respectively-find-the-total-first-order-dispersion\/","title":{"rendered":"The dispersion due to material, waveguide and profile are -2.8nm-1km-1, 20.1nm-1km-1 and 23.2nm-1km-1 respectively. Find the total first order dispersion?"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a975655b9dcc\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    36.2psnm-1 km-1                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    38.12psnm-1 km-1                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    40.5psnm-1 km-1                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    20.9psnm-1 km-1                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is A. 36.2psnm-1 km-1.<\/p>\n<p>The total first order dispersion is the sum of the material, waveguide, and profile dispersions. The material dispersion is the change in the refractive index with respect to the wavelength of light. The waveguide dispersion is the change in the refractive index with respect to the frequency of light. The profile dispersion is the change in the refractive index with respect to the position of the light in the waveguide.<\/p>\n<p>The material dispersion is given by the following equation:<\/p>\n<p>$$\\frac{d\\beta}{d\\lambda} = -\\frac{n_2}{c}$$<\/p>\n<p>where $n_2$ is the group refractive index and $c$ is the speed of light in a vacuum.<\/p>\n<p>The waveguide dispersion is given by the following equation:<\/p>\n<p>$$\\frac{d\\beta}{d\\omega} = -\\frac{n_g}{c}$$<\/p>\n<p>where $n_g$ is the group refractive index of the waveguide.<\/p>\n<p>The profile dispersion is given by the following equation:<\/p>\n<p>$$\\frac{d\\beta}{dz} = <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n  <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>               <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> -\\frac{n_p}{c}$$<\/p>\n<p>where $n_p$ is the profile refractive index.<\/p>\n<p>The total first order dispersion is given by the following equation:<\/p>\n<p>$$\\frac{d\\beta}{d\\lambda} = \\frac{d\\beta}{d\\omega} + \\frac{d\\beta}{dz}$$<\/p>\n<p>Substituting the equations for the material, waveguide, and profile dispersions into this equation, we get the following equation:<\/p>\n<p>$$\\frac{d\\beta}{d\\lambda} = -\\frac{n_2}{c} &#8211; \\frac{n_g}{c} &#8211; \\frac{n_p}{c}$$<\/p>\n<p>The values for the material, waveguide, and profile dispersions are given in the question. Substituting these values into the equation, we get the following equation:<\/p>\n<p>$$\\frac{d\\beta}{d\\lambda} = -\\frac{2.8}{c} + \\frac{20.1}{c} + \\frac{23.2}{c} = 36.2\\text{ ps\/nm\/km}$$<\/p>\n<p>Therefore, the total first order dispersion is 36.2psnm-1 km-1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[684],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The dispersion due to material, waveguide and profile are -2.8nm-1km-1, 20.1nm-1km-1 and 23.2nm-1km-1 respectively. 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