{"id":8302,"date":"2024-04-15T02:58:19","date_gmt":"2024-04-15T02:58:19","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=8302"},"modified":"2024-04-15T02:58:19","modified_gmt":"2024-04-15T02:58:19","slug":"the-scale-of-a-tilted-photograph-of-focal-length-f-taken-from-an-altitude-h-along-the-plate-parallel-through-principal-point-is-a-fractextftexthsec-theta-b-frac","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-scale-of-a-tilted-photograph-of-focal-length-f-taken-from-an-altitude-h-along-the-plate-parallel-through-principal-point-is-a-fractextftexthsec-theta-b-frac\/","title":{"rendered":"The scale of a tilted photograph of focal length f taken from an altitude H, along the plate parallel through principal point is A. $$\\frac{{\\text{f}}}{{{\\text{H}}\\sec \\theta }}$$ B. $$\\frac{{{\\text{f}}\\sec \\theta }}{{\\text{H}}}$$ C. $$\\frac{{\\text{f}}}{{\\text{H}}}$$ D. $$\\frac{{\\text{f}}}{{{\\text{H}}\\cos \\frac{1}{2}\\theta }}$$"},"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_6a9b432b2d68f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{f}}}{{{\text{H}}sec \theta }}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"true\">\r\n                    $$\frac{{{\text{f}}sec \theta }}{{\text{H}}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{f}}}{{\text{H}}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{{\text{f}}}{{{\text{H}}cos \frac{1}{2}\theta }}$$                <\/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 $\\boxed{\\frac{{\\text{f}}}{{{\\text{H}}\\sec \\theta }}}$.<\/p>\n<p>The scale of a photograph is the ratio of the distance between two objects on the photograph to the distance between the same two objects on the ground. In the case of a tilted photograph, the scale is not constant, but varies depending on the angle of the camera to the ground.<\/p>\n<p>The formula for the scale of a tilted photograph is:<\/p>\n<p>$$\\text{Scale} = \\frac{{\\text{f}}}{{{\\text{H}}\\sec \\theta }}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$f$ is the focal length of the camera<\/li>\n<li>$H$ is the altitude of the camera<\/li>\n<li>$\\theta$ is the angle of the camera to the ground<\/li>\n<\/ul>\n<p>The scale is greatest when the camera is perpendicular to the ground, and decreases as the camera is tilted. This is because the distance between two objects on the photograph is greater when the camera is tilted, so the scale must be smaller to compensate.<\/p>\n<p>Option A is incorrect because it does not include the factor of $\\sec \\theta$. Option B is incorrect because it does not include the factor of $f$. Option C is incorrect because it does not include the factor of <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 <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> 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                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> $\\theta$. Option D is incorrect because it does not include the factor of $f$ or $\\theta$.<\/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":[654],"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 scale of a tilted photograph of focal length f taken from an altitude H, along the plate parallel through principal point is A. $$\\frac{{\\text{f}}}{{{\\text{H}}\\sec \\theta }}$$ B. $$\\frac{{{\\text{f}}\\sec \\theta }}{{\\text{H}}}$$ C. $$\\frac{{\\text{f}}}{{\\text{H}}}$$ D. $$\\frac{{\\text{f}}}{{{\\text{H}}\\cos \\frac{1}{2}\\theta }}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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