{"id":8256,"date":"2024-04-15T02:57:31","date_gmt":"2024-04-15T02:57:31","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=8256"},"modified":"2024-04-15T02:57:31","modified_gmt":"2024-04-15T02:57:31","slug":"the-maximum-error-in-radial-line-assumption-is-a-fractexthtexthtextftan-theta-b-fractexthtexthtextf2tan-theta-c-fractex","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-maximum-error-in-radial-line-assumption-is-a-fractexthtexthtextftan-theta-b-fractexthtexthtextf2tan-theta-c-fractex\/","title":{"rendered":"The maximum error in radial line assumption, is A. $$\\frac{{\\text{h}}}{{\\text{H}}}{\\text{f}}\\tan \\theta $$ B. $$\\frac{{\\text{h}}}{{\\text{H}}}{{\\text{f}}^2}\\tan \\theta $$ C. $$\\frac{{\\text{h}}}{{\\text{H}}}{{\\text{f}}^2}\\sin \\theta $$ D. $$\\frac{{\\text{h}}}{{\\text{H}}}{\\text{f}}\\cos \\theta $$"},"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_6a9dc48870e34\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    $$\frac{{\text{h}}}{{\text{H}}}{\text{f}}\tan \theta $$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{h}}}{{\text{H}}}{{\text{f}}^2}\tan \theta $$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{h}}}{{\text{H}}}{{\text{f}}^2}sin \theta $$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{h}}}{{\text{H}}}{\text{f}}cos \theta $$                <\/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 $\\frac{{\\text{h}}}{{\\text{H}}}{\\text{f}}\\tan \\theta$.<\/p>\n<p>The radial line assumption is a simplification that is often used in optics and other fields. It assumes that light travels in straight lines from a source to an observer. This assumption is valid for small angles, but it can lead to errors for large angles.<\/p>\n<p>The maximum error in the radial line assumption is given by the following equation:<\/p>\n<p>$$\\Delta \\theta = \\frac{{\\text{h}}}{{\\text{H}}}{\\text{f}}\\tan \\theta$$<\/p>\n<p>where $\\Delta \\theta$ is the maximum error, $h$ is the height of the object, $H$ is the distance to the object, $f$ is the focal length of the lens, and $\\theta$ is the angle between the object and the line of sight.<\/p>\n<p>The equation shows that the maximum error is proportional to the height of the object, the focal length of the lens, and the tangent of the angle between the object and the line of sight. The error is also inversely proportional to the distance to the object.<\/p>\n<p>The radial line assumption is a useful simplification, but it is important to be aware of its limitations. The maximum error can be significant for large angles, so it <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 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